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 </pre><pre class="rust"><code><span class="comment">// Copyright 2018 Developers of the Rand project.</span>
 <span class="comment">// Copyright 2013 The Rust Project Developers.</span>
 <span class="comment">//</span>
 <span class="comment">// Licensed under the Apache License, Version 2.0 &lt;LICENSE-APACHE or</span>
 <span class="comment">// https://www.apache.org/licenses/LICENSE-2.0&gt; or the MIT license</span>
 <span class="comment">// &lt;LICENSE-MIT or https://opensource.org/licenses/MIT&gt;, at your</span>
 <span class="comment">// option. This file may not be copied, modified, or distributed</span>
 <span class="comment">// except according to those terms.</span>

 <span class="doccomment">//! The Gamma and derived distributions.</span>

 <span class="comment">// We use the variable names from the published reference, therefore this</span>
 <span class="comment">// warning is not helpful.</span>
 <span class="attribute">#![<span class="ident">allow</span>(<span class="ident">clippy::many_single_char_names</span>)]</span>

 <span class="kw">use</span> <span class="ident"><span class="self">self</span>::ChiSquaredRepr</span>::<span class="kw-2">*</span>;
 <span class="kw">use</span> <span class="ident"><span class="self">self</span>::GammaRepr</span>::<span class="kw-2">*</span>;

 <span class="kw">use</span> <span class="ident"><span class="kw">crate</span>::normal::StandardNormal</span>;
 <span class="kw">use</span> <span class="ident">num_traits::Float</span>;
 <span class="kw">use</span> <span class="kw">crate</span>::{<span class="ident">Distribution</span>, <span class="ident">Exp</span>, <span class="ident">Exp1</span>, <span class="ident">Open01</span>};
 <span class="kw">use</span> <span class="ident">rand::Rng</span>;
 <span class="kw">use</span> <span class="ident">core::fmt</span>;
 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>)]</span>
 <span class="kw">use</span> <span class="ident">serde</span>::{<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>};

 <span class="doccomment">/// The Gamma distribution `Gamma(shape, scale)` distribution.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// The density function of this distribution is</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// ```text</span>
 <span class="doccomment">/// f(x) =  x^(k - 1) * exp(-x / θ) / (Γ(k) * θ^k)</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// where `Γ` is the Gamma function, `k` is the shape and `θ` is the</span>
 <span class="doccomment">/// scale and both `k` and `θ` are strictly positive.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// The algorithm used is that described by Marsaglia &amp; Tsang 2000[^1],</span>
 <span class="doccomment">/// falling back to directly sampling from an Exponential for `shape</span>
 <span class="doccomment">/// == 1`, and using the boosting technique described in that paper for</span>
 <span class="doccomment">/// `shape &lt; 1`.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// # Example</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">/// use rand_distr::{Distribution, Gamma};</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// let gamma = Gamma::new(2.0, 5.0).unwrap();</span>
 <span class="doccomment">/// let v = gamma.sample(&amp;mut rand::thread_rng());</span>
 <span class="doccomment">/// println!(&quot;{} is from a Gamma(2, 5) distribution&quot;, v);</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// [^1]: George Marsaglia and Wai Wan Tsang. 2000. &quot;A Simple Method for</span>
 <span class="doccomment">///       Generating Gamma Variables&quot; *ACM Trans. Math. Softw.* 26, 3</span>
 <span class="doccomment">///       (September 2000), 363-372.</span>
 <span class="doccomment">///       DOI:[10.1145/358407.358414](https://doi.acm.org/10.1145/358407.358414)</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Gamma</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">repr</span>: <span class="ident">GammaRepr</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 }

 <span class="doccomment">/// Error type returned from `Gamma::new`.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
 <span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">Error</span> {
     <span class="doccomment">/// `shape &lt;= 0` or `nan`.</span>
     <span class="ident">ShapeTooSmall</span>,
     <span class="doccomment">/// `scale &lt;= 0` or `nan`.</span>
     <span class="ident">ScaleTooSmall</span>,
     <span class="doccomment">/// `1 / scale == 0`.</span>
     <span class="ident">ScaleTooLarge</span>,
 }

 <span class="kw">impl</span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">Error</span> {
     <span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&amp;mut</span> <span class="ident">fmt::Formatter</span><span class="op">&lt;</span><span class="lifetime">&#39;_</span><span class="op">&gt;</span>) -&gt; <span class="ident">fmt::Result</span> {
         <span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
             <span class="ident">Error::ShapeTooSmall</span> =&gt; <span class="string">&quot;shape is not positive in gamma distribution&quot;</span>,
             <span class="ident">Error::ScaleTooSmall</span> =&gt; <span class="string">&quot;scale is not positive in gamma distribution&quot;</span>,
             <span class="ident">Error::ScaleTooLarge</span> =&gt; <span class="string">&quot;scale is infinity in gamma distribution&quot;</span>,
         })
     }
 }

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)))]</span>
 <span class="kw">impl</span> <span class="ident">std::error::Error</span> <span class="kw">for</span> <span class="ident">Error</span> {}

 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">enum</span> <span class="ident">GammaRepr</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">Large</span>(<span class="ident">GammaLargeShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>),
     <span class="ident">One</span>(<span class="ident">Exp</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>),
     <span class="ident">Small</span>(<span class="ident">GammaSmallShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>),
 }

 <span class="comment">// These two helpers could be made public, but saving the</span>
 <span class="comment">// match-on-Gamma-enum branch from using them directly (e.g. if one</span>
 <span class="comment">// knows that the shape is always &gt; 1) doesn&#39;t appear to be much</span>
 <span class="comment">// faster.</span>

 <span class="doccomment">/// Gamma distribution where the shape parameter is less than 1.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// Note, samples from this require a compulsory floating-point `pow`</span>
 <span class="doccomment">/// call, which makes it significantly slower than sampling from a</span>
 <span class="doccomment">/// gamma distribution where the shape parameter is greater than or</span>
 <span class="doccomment">/// equal to 1.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// See `Gamma` for sampling from a Gamma distribution with general</span>
 <span class="doccomment">/// shape parameters.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">struct</span> <span class="ident">GammaSmallShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">inv_shape</span>: <span class="ident">F</span>,
     <span class="ident">large_shape</span>: <span class="ident">GammaLargeShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 }

 <span class="doccomment">/// Gamma distribution where the shape parameter is larger than 1.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// See `Gamma` for sampling from a Gamma distribution with general</span>
 <span class="doccomment">/// shape parameters.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">struct</span> <span class="ident">GammaLargeShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">scale</span>: <span class="ident">F</span>,
     <span class="ident">c</span>: <span class="ident">F</span>,
     <span class="ident">d</span>: <span class="ident">F</span>,
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Gamma</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="doccomment">/// Construct an object representing the `Gamma(shape, scale)`</span>
     <span class="doccomment">/// distribution.</span>
     <span class="attribute">#[<span class="ident">inline</span>]</span>
     <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">shape</span>: <span class="ident">F</span>, <span class="ident">scale</span>: <span class="ident">F</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">Gamma</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>, <span class="ident">Error</span><span class="op">&gt;</span> {
         <span class="kw">if</span> <span class="op">!</span>(<span class="ident">shape</span> <span class="op">&gt;</span> <span class="ident">F::zero</span>()) {
             <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::ShapeTooSmall</span>);
         }
         <span class="kw">if</span> <span class="op">!</span>(<span class="ident">scale</span> <span class="op">&gt;</span> <span class="ident">F::zero</span>()) {
             <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error::ScaleTooSmall</span>);
         }

         <span class="kw">let</span> <span class="ident">repr</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">shape</span> <span class="op">==</span> <span class="ident">F::one</span>() {
             <span class="ident">One</span>(<span class="ident">Exp::new</span>(<span class="ident">F::one</span>() <span class="op">/</span> <span class="ident">scale</span>).<span class="ident">map_err</span>(<span class="op">|</span><span class="kw">_</span><span class="op">|</span> <span class="ident">Error::ScaleTooLarge</span>)<span class="question-mark">?</span>)
         } <span class="kw">else</span> <span class="kw">if</span> <span class="ident">shape</span> <span class="op">&lt;</span> <span class="ident">F::one</span>() {
             <span class="ident">Small</span>(<span class="ident">GammaSmallShape::new_raw</span>(<span class="ident">shape</span>, <span class="ident">scale</span>))
         } <span class="kw">else</span> {
             <span class="ident">Large</span>(<span class="ident">GammaLargeShape::new_raw</span>(<span class="ident">shape</span>, <span class="ident">scale</span>))
         };
         <span class="prelude-val">Ok</span>(<span class="ident">Gamma</span> { <span class="ident">repr</span> })
     }
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">GammaSmallShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">new_raw</span>(<span class="ident">shape</span>: <span class="ident">F</span>, <span class="ident">scale</span>: <span class="ident">F</span>) -&gt; <span class="ident">GammaSmallShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> {
         <span class="ident">GammaSmallShape</span> {
             <span class="ident">inv_shape</span>: <span class="ident">F::one</span>() <span class="op">/</span> <span class="ident">shape</span>,
             <span class="ident">large_shape</span>: <span class="ident">GammaLargeShape::new_raw</span>(<span class="ident">shape</span> <span class="op">+</span> <span class="ident">F::one</span>(), <span class="ident">scale</span>),
         }
     }
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">GammaLargeShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">new_raw</span>(<span class="ident">shape</span>: <span class="ident">F</span>, <span class="ident">scale</span>: <span class="ident">F</span>) -&gt; <span class="ident">GammaLargeShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> {
         <span class="kw">let</span> <span class="ident">d</span> <span class="op">=</span> <span class="ident">shape</span> <span class="op">-</span> <span class="ident">F::from</span>(<span class="number">1.</span> <span class="op">/</span> <span class="number">3.</span>).<span class="ident">unwrap</span>();
         <span class="ident">GammaLargeShape</span> {
             <span class="ident">scale</span>,
             <span class="ident">c</span>: <span class="ident">F::one</span>() <span class="op">/</span> (<span class="ident">F::from</span>(<span class="number">9.</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">d</span>).<span class="ident">sqrt</span>(),
             <span class="ident">d</span>,
         }
     }
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Gamma</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="kw">match</span> <span class="self">self</span>.<span class="ident">repr</span> {
             <span class="ident">Small</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) =&gt; <span class="ident">g</span>.<span class="ident">sample</span>(<span class="ident">rng</span>),
             <span class="ident">One</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) =&gt; <span class="ident">g</span>.<span class="ident">sample</span>(<span class="ident">rng</span>),
             <span class="ident">Large</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) =&gt; <span class="ident">g</span>.<span class="ident">sample</span>(<span class="ident">rng</span>),
         }
     }
 }
 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">GammaSmallShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">F</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);

         <span class="self">self</span>.<span class="ident">large_shape</span>.<span class="ident">sample</span>(<span class="ident">rng</span>) <span class="op">*</span> <span class="ident">u</span>.<span class="ident">powf</span>(<span class="self">self</span>.<span class="ident">inv_shape</span>)
     }
 }
 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">GammaLargeShape</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="comment">// Marsaglia &amp; Tsang method, 2000</span>
         <span class="kw">loop</span> {
             <span class="kw">let</span> <span class="ident">x</span>: <span class="ident">F</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">StandardNormal</span>);
             <span class="kw">let</span> <span class="ident">v_cbrt</span> <span class="op">=</span> <span class="ident">F::one</span>() <span class="op">+</span> <span class="self">self</span>.<span class="ident">c</span> <span class="op">*</span> <span class="ident">x</span>;
             <span class="kw">if</span> <span class="ident">v_cbrt</span> <span class="op">&lt;</span><span class="op">=</span> <span class="ident">F::zero</span>() {
                 <span class="comment">// a^3 &lt;= 0 iff a &lt;= 0</span>
                 <span class="kw">continue</span>;
             }

             <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">v_cbrt</span> <span class="op">*</span> <span class="ident">v_cbrt</span> <span class="op">*</span> <span class="ident">v_cbrt</span>;
             <span class="kw">let</span> <span class="ident">u</span>: <span class="ident">F</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);

             <span class="kw">let</span> <span class="ident">x_sqr</span> <span class="op">=</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>;
             <span class="kw">if</span> <span class="ident">u</span> <span class="op">&lt;</span> <span class="ident">F::one</span>() <span class="op">-</span> <span class="ident">F::from</span>(<span class="number">0.0331</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">x_sqr</span> <span class="op">*</span> <span class="ident">x_sqr</span>
                 <span class="op">|</span><span class="op">|</span> <span class="ident">u</span>.<span class="ident">ln</span>() <span class="op">&lt;</span> <span class="ident">F::from</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">x_sqr</span> <span class="op">+</span> <span class="self">self</span>.<span class="ident">d</span> <span class="op">*</span> (<span class="ident">F::one</span>() <span class="op">-</span> <span class="ident">v</span> <span class="op">+</span> <span class="ident">v</span>.<span class="ident">ln</span>())
             {
                 <span class="kw">return</span> <span class="self">self</span>.<span class="ident">d</span> <span class="op">*</span> <span class="ident">v</span> <span class="op">*</span> <span class="self">self</span>.<span class="ident">scale</span>;
             }
         }
     }
 }

 <span class="doccomment">/// The chi-squared distribution `χ²(k)`, where `k` is the degrees of</span>
 <span class="doccomment">/// freedom.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// For `k &gt; 0` integral, this distribution is the sum of the squares</span>
 <span class="doccomment">/// of `k` independent standard normal random variables. For other</span>
 <span class="doccomment">/// `k`, this uses the equivalent characterisation</span>
 <span class="doccomment">/// `χ²(k) = Gamma(k/2, 2)`.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// # Example</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">/// use rand_distr::{ChiSquared, Distribution};</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// let chi = ChiSquared::new(11.0).unwrap();</span>
 <span class="doccomment">/// let v = chi.sample(&amp;mut rand::thread_rng());</span>
 <span class="doccomment">/// println!(&quot;{} is from a χ²(11) distribution&quot;, v)</span>
 <span class="doccomment">/// ```</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">repr</span>: <span class="ident">ChiSquaredRepr</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 }

 <span class="doccomment">/// Error type returned from `ChiSquared::new` and `StudentT::new`.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">ChiSquaredError</span> {
     <span class="doccomment">/// `0.5 * k &lt;= 0` or `nan`.</span>
     <span class="ident">DoFTooSmall</span>,
 }

 <span class="kw">impl</span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">ChiSquaredError</span> {
     <span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&amp;mut</span> <span class="ident">fmt::Formatter</span><span class="op">&lt;</span><span class="lifetime">&#39;_</span><span class="op">&gt;</span>) -&gt; <span class="ident">fmt::Result</span> {
         <span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
             <span class="ident">ChiSquaredError::DoFTooSmall</span> =&gt; {
                 <span class="string">&quot;degrees-of-freedom k is not positive in chi-squared distribution&quot;</span>
             }
         })
     }
 }

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)))]</span>
 <span class="kw">impl</span> <span class="ident">std::error::Error</span> <span class="kw">for</span> <span class="ident">ChiSquaredError</span> {}

 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">enum</span> <span class="ident">ChiSquaredRepr</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="comment">// k == 1, Gamma(alpha, ..) is particularly slow for alpha &lt; 1,</span>
     <span class="comment">// e.g. when alpha = 1/2 as it would be for this case, so special-</span>
     <span class="comment">// casing and using the definition of N(0,1)^2 is faster.</span>
     <span class="ident">DoFExactlyOne</span>,
     <span class="ident">DoFAnythingElse</span>(<span class="ident">Gamma</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>),
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="doccomment">/// Create a new chi-squared distribution with degrees-of-freedom</span>
     <span class="doccomment">/// `k`.</span>
     <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">k</span>: <span class="ident">F</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>, <span class="ident">ChiSquaredError</span><span class="op">&gt;</span> {
         <span class="kw">let</span> <span class="ident">repr</span> <span class="op">=</span> <span class="kw">if</span> <span class="ident">k</span> <span class="op">==</span> <span class="ident">F::one</span>() {
             <span class="ident">DoFExactlyOne</span>
         } <span class="kw">else</span> {
             <span class="kw">if</span> <span class="op">!</span>(<span class="ident">F::from</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">k</span> <span class="op">&gt;</span> <span class="ident">F::zero</span>()) {
                 <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">ChiSquaredError::DoFTooSmall</span>);
             }
             <span class="ident">DoFAnythingElse</span>(<span class="ident">Gamma::new</span>(<span class="ident">F::from</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">k</span>, <span class="ident">F::from</span>(<span class="number">2.0</span>).<span class="ident">unwrap</span>()).<span class="ident">unwrap</span>())
         };
         <span class="prelude-val">Ok</span>(<span class="ident">ChiSquared</span> { <span class="ident">repr</span> })
     }
 }
 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="kw">match</span> <span class="self">self</span>.<span class="ident">repr</span> {
             <span class="ident">DoFExactlyOne</span> =&gt; {
                 <span class="comment">// k == 1 =&gt; N(0,1)^2</span>
                 <span class="kw">let</span> <span class="ident">norm</span>: <span class="ident">F</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">StandardNormal</span>);
                 <span class="ident">norm</span> <span class="op">*</span> <span class="ident">norm</span>
             }
             <span class="ident">DoFAnythingElse</span>(<span class="kw-2">ref</span> <span class="ident">g</span>) =&gt; <span class="ident">g</span>.<span class="ident">sample</span>(<span class="ident">rng</span>),
         }
     }
 }

 <span class="doccomment">/// The Fisher F distribution `F(m, n)`.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// This distribution is equivalent to the ratio of two normalised</span>
 <span class="doccomment">/// chi-squared distributions, that is, `F(m,n) = (χ²(m)/m) /</span>
 <span class="doccomment">/// (χ²(n)/n)`.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// # Example</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">/// use rand_distr::{FisherF, Distribution};</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// let f = FisherF::new(2.0, 32.0).unwrap();</span>
 <span class="doccomment">/// let v = f.sample(&amp;mut rand::thread_rng());</span>
 <span class="doccomment">/// println!(&quot;{} is from an F(2, 32) distribution&quot;, v)</span>
 <span class="doccomment">/// ```</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">FisherF</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">numer</span>: <span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">denom</span>: <span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="comment">// denom_dof / numer_dof so that this can just be a straight</span>
     <span class="comment">// multiplication, rather than a division.</span>
     <span class="ident">dof_ratio</span>: <span class="ident">F</span>,
 }

 <span class="doccomment">/// Error type returned from `FisherF::new`.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">FisherFError</span> {
     <span class="doccomment">/// `m &lt;= 0` or `nan`.</span>
     <span class="ident">MTooSmall</span>,
     <span class="doccomment">/// `n &lt;= 0` or `nan`.</span>
     <span class="ident">NTooSmall</span>,
 }

 <span class="kw">impl</span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">FisherFError</span> {
     <span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&amp;mut</span> <span class="ident">fmt::Formatter</span><span class="op">&lt;</span><span class="lifetime">&#39;_</span><span class="op">&gt;</span>) -&gt; <span class="ident">fmt::Result</span> {
         <span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
             <span class="ident">FisherFError::MTooSmall</span> =&gt; <span class="string">&quot;m is not positive in Fisher F distribution&quot;</span>,
             <span class="ident">FisherFError::NTooSmall</span> =&gt; <span class="string">&quot;n is not positive in Fisher F distribution&quot;</span>,
         })
     }
 }

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)))]</span>
 <span class="kw">impl</span> <span class="ident">std::error::Error</span> <span class="kw">for</span> <span class="ident">FisherFError</span> {}

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">FisherF</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="doccomment">/// Create a new `FisherF` distribution, with the given parameter.</span>
     <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">m</span>: <span class="ident">F</span>, <span class="ident">n</span>: <span class="ident">F</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">FisherF</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>, <span class="ident">FisherFError</span><span class="op">&gt;</span> {
         <span class="kw">let</span> <span class="ident">zero</span> <span class="op">=</span> <span class="ident">F::zero</span>();
         <span class="kw">if</span> <span class="op">!</span>(<span class="ident">m</span> <span class="op">&gt;</span> <span class="ident">zero</span>) {
             <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">FisherFError::MTooSmall</span>);
         }
         <span class="kw">if</span> <span class="op">!</span>(<span class="ident">n</span> <span class="op">&gt;</span> <span class="ident">zero</span>) {
             <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">FisherFError::NTooSmall</span>);
         }

         <span class="prelude-val">Ok</span>(<span class="ident">FisherF</span> {
             <span class="ident">numer</span>: <span class="ident">ChiSquared::new</span>(<span class="ident">m</span>).<span class="ident">unwrap</span>(),
             <span class="ident">denom</span>: <span class="ident">ChiSquared::new</span>(<span class="ident">n</span>).<span class="ident">unwrap</span>(),
             <span class="ident">dof_ratio</span>: <span class="ident">n</span> <span class="op">/</span> <span class="ident">m</span>,
         })
     }
 }
 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">FisherF</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="self">self</span>.<span class="ident">numer</span>.<span class="ident">sample</span>(<span class="ident">rng</span>) <span class="op">/</span> <span class="self">self</span>.<span class="ident">denom</span>.<span class="ident">sample</span>(<span class="ident">rng</span>) <span class="op">*</span> <span class="self">self</span>.<span class="ident">dof_ratio</span>
     }
 }

 <span class="doccomment">/// The Student t distribution, `t(nu)`, where `nu` is the degrees of</span>
 <span class="doccomment">/// freedom.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// # Example</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">/// use rand_distr::{StudentT, Distribution};</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// let t = StudentT::new(11.0).unwrap();</span>
 <span class="doccomment">/// let v = t.sample(&amp;mut rand::thread_rng());</span>
 <span class="doccomment">/// println!(&quot;{} is from a t(11) distribution&quot;, v)</span>
 <span class="doccomment">/// ```</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">StudentT</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">chi</span>: <span class="ident">ChiSquared</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">dof</span>: <span class="ident">F</span>,
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">StudentT</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="doccomment">/// Create a new Student t distribution with `n` degrees of</span>
     <span class="doccomment">/// freedom.</span>
     <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">n</span>: <span class="ident">F</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">StudentT</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>, <span class="ident">ChiSquaredError</span><span class="op">&gt;</span> {
         <span class="prelude-val">Ok</span>(<span class="ident">StudentT</span> {
             <span class="ident">chi</span>: <span class="ident">ChiSquared::new</span>(<span class="ident">n</span>)<span class="question-mark">?</span>,
             <span class="ident">dof</span>: <span class="ident">n</span>,
         })
     }
 }
 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">StudentT</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">StandardNormal</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Exp1</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="kw">let</span> <span class="ident">norm</span>: <span class="ident">F</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">StandardNormal</span>);
         <span class="ident">norm</span> <span class="op">*</span> (<span class="self">self</span>.<span class="ident">dof</span> <span class="op">/</span> <span class="self">self</span>.<span class="ident">chi</span>.<span class="ident">sample</span>(<span class="ident">rng</span>)).<span class="ident">sqrt</span>()
     }
 }

 <span class="doccomment">/// The algorithm used for sampling the Beta distribution.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// Reference:</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// R. C. H. Cheng (1978).</span>
 <span class="doccomment">/// Generating beta variates with nonintegral shape parameters.</span>
 <span class="doccomment">/// Communications of the ACM 21, 317-322.</span>
 <span class="doccomment">/// https://doi.org/10.1145/359460.359482</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">enum</span> <span class="ident">BetaAlgorithm</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span> {
     <span class="ident">BB</span>(<span class="ident">BB</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>),
     <span class="ident">BC</span>(<span class="ident">BC</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>),
 }

 <span class="doccomment">/// Algorithm BB for `min(alpha, beta) &gt; 1`.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">struct</span> <span class="ident">BB</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span> {
     <span class="ident">alpha</span>: <span class="ident">N</span>,
     <span class="ident">beta</span>: <span class="ident">N</span>,
     <span class="ident">gamma</span>: <span class="ident">N</span>,
 }

 <span class="doccomment">/// Algorithm BC for `min(alpha, beta) &lt;= 1`.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">struct</span> <span class="ident">BC</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span> {
     <span class="ident">alpha</span>: <span class="ident">N</span>,
     <span class="ident">beta</span>: <span class="ident">N</span>,
     <span class="ident">delta</span>: <span class="ident">N</span>,
     <span class="ident">kappa1</span>: <span class="ident">N</span>,
     <span class="ident">kappa2</span>: <span class="ident">N</span>,
 }

 <span class="doccomment">/// The Beta distribution with shape parameters `alpha` and `beta`.</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// # Example</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// ```</span>
 <span class="doccomment">/// use rand_distr::{Distribution, Beta};</span>
 <span class="doccomment">///</span>
 <span class="doccomment">/// let beta = Beta::new(2.0, 5.0).unwrap();</span>
 <span class="doccomment">/// let v = beta.sample(&amp;mut rand::thread_rng());</span>
 <span class="doccomment">/// println!(&quot;{} is from a Beta(2, 5) distribution&quot;, v);</span>
 <span class="doccomment">/// ```</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Beta</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="ident">a</span>: <span class="ident">F</span>, <span class="ident">b</span>: <span class="ident">F</span>, <span class="ident">switched_params</span>: <span class="ident">bool</span>,
     <span class="ident">algorithm</span>: <span class="ident">BetaAlgorithm</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 }

 <span class="doccomment">/// Error type returned from `Beta::new`.</span>
 <span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;serde1&quot;</span>, <span class="ident">derive</span>(<span class="ident">Serialize</span>, <span class="ident">Deserialize</span>))]</span>
 <span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">BetaError</span> {
     <span class="doccomment">/// `alpha &lt;= 0` or `nan`.</span>
     <span class="ident">AlphaTooSmall</span>,
     <span class="doccomment">/// `beta &lt;= 0` or `nan`.</span>
     <span class="ident">BetaTooSmall</span>,
 }

 <span class="kw">impl</span> <span class="ident">fmt::Display</span> <span class="kw">for</span> <span class="ident">BetaError</span> {
     <span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&amp;mut</span> <span class="ident">fmt::Formatter</span><span class="op">&lt;</span><span class="lifetime">&#39;_</span><span class="op">&gt;</span>) -&gt; <span class="ident">fmt::Result</span> {
         <span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
             <span class="ident">BetaError::AlphaTooSmall</span> =&gt; <span class="string">&quot;alpha is not positive in beta distribution&quot;</span>,
             <span class="ident">BetaError::BetaTooSmall</span> =&gt; <span class="string">&quot;beta is not positive in beta distribution&quot;</span>,
         })
     }
 }

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)]</span>
 <span class="attribute">#[<span class="ident">cfg_attr</span>(<span class="ident">doc_cfg</span>, <span class="ident">doc</span>(<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;std&quot;</span>)))]</span>
 <span class="kw">impl</span> <span class="ident">std::error::Error</span> <span class="kw">for</span> <span class="ident">BetaError</span> {}

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Beta</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="doccomment">/// Construct an object representing the `Beta(alpha, beta)`</span>
     <span class="doccomment">/// distribution.</span>
     <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">alpha</span>: <span class="ident">F</span>, <span class="ident">beta</span>: <span class="ident">F</span>) -&gt; <span class="prelude-ty">Result</span><span class="op">&lt;</span><span class="ident">Beta</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>, <span class="ident">BetaError</span><span class="op">&gt;</span> {
         <span class="kw">if</span> <span class="op">!</span>(<span class="ident">alpha</span> <span class="op">&gt;</span> <span class="ident">F::zero</span>()) {
             <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">BetaError::AlphaTooSmall</span>);
         }
         <span class="kw">if</span> <span class="op">!</span>(<span class="ident">beta</span> <span class="op">&gt;</span> <span class="ident">F::zero</span>()) {
             <span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">BetaError::BetaTooSmall</span>);
         }
         <span class="comment">// From now on, we use the notation from the reference,</span>
         <span class="comment">// i.e. `alpha` and `beta` are renamed to `a0` and `b0`.</span>
         <span class="kw">let</span> (<span class="ident">a0</span>, <span class="ident">b0</span>) <span class="op">=</span> (<span class="ident">alpha</span>, <span class="ident">beta</span>);
         <span class="kw">let</span> (<span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">switched_params</span>) <span class="op">=</span> <span class="kw">if</span> <span class="ident">a0</span> <span class="op">&lt;</span> <span class="ident">b0</span> {
             (<span class="ident">a0</span>, <span class="ident">b0</span>, <span class="bool-val">false</span>)
         } <span class="kw">else</span> {
             (<span class="ident">b0</span>, <span class="ident">a0</span>, <span class="bool-val">true</span>)
         };
         <span class="kw">if</span> <span class="ident">a</span> <span class="op">&gt;</span> <span class="ident">F::one</span>() {
             <span class="comment">// Algorithm BB</span>
             <span class="kw">let</span> <span class="ident">alpha</span> <span class="op">=</span> <span class="ident">a</span> <span class="op">+</span> <span class="ident">b</span>;
             <span class="kw">let</span> <span class="ident">beta</span> <span class="op">=</span> ((<span class="ident">alpha</span> <span class="op">-</span> <span class="ident">F::from</span>(<span class="number">2.</span>).<span class="ident">unwrap</span>())
                         <span class="op">/</span> (<span class="ident">F::from</span>(<span class="number">2.</span>).<span class="ident">unwrap</span>()<span class="kw-2">*</span><span class="ident">a</span><span class="kw-2">*</span><span class="ident">b</span> <span class="op">-</span> <span class="ident">alpha</span>)).<span class="ident">sqrt</span>();
             <span class="kw">let</span> <span class="ident">gamma</span> <span class="op">=</span> <span class="ident">a</span> <span class="op">+</span> <span class="ident">F::one</span>() <span class="op">/</span> <span class="ident">beta</span>;

             <span class="prelude-val">Ok</span>(<span class="ident">Beta</span> {
                 <span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">switched_params</span>,
                 <span class="ident">algorithm</span>: <span class="ident">BetaAlgorithm::BB</span>(<span class="ident">BB</span> {
                     <span class="ident">alpha</span>, <span class="ident">beta</span>, <span class="ident">gamma</span>,
                 })
             })
         } <span class="kw">else</span> {
             <span class="comment">// Algorithm BC</span>
             <span class="comment">//</span>
             <span class="comment">// Here `a` is the maximum instead of the minimum.</span>
             <span class="kw">let</span> (<span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">switched_params</span>) <span class="op">=</span> (<span class="ident">b</span>, <span class="ident">a</span>, <span class="op">!</span><span class="ident">switched_params</span>);
             <span class="kw">let</span> <span class="ident">alpha</span> <span class="op">=</span> <span class="ident">a</span> <span class="op">+</span> <span class="ident">b</span>;
             <span class="kw">let</span> <span class="ident">beta</span> <span class="op">=</span> <span class="ident">F::one</span>() <span class="op">/</span> <span class="ident">b</span>;
             <span class="kw">let</span> <span class="ident">delta</span> <span class="op">=</span> <span class="ident">F::one</span>() <span class="op">+</span> <span class="ident">a</span> <span class="op">-</span> <span class="ident">b</span>;
             <span class="kw">let</span> <span class="ident">kappa1</span> <span class="op">=</span> <span class="ident">delta</span>
                 <span class="op">*</span> (<span class="ident">F::from</span>(<span class="number">1.</span> <span class="op">/</span> <span class="number">18.</span> <span class="op">/</span> <span class="number">4.</span>).<span class="ident">unwrap</span>() <span class="op">+</span> <span class="ident">F::from</span>(<span class="number">3.</span> <span class="op">/</span> <span class="number">18.</span> <span class="op">/</span> <span class="number">4.</span>).<span class="ident">unwrap</span>()<span class="kw-2">*</span><span class="ident">b</span>)
                 <span class="op">/</span> (<span class="ident">a</span><span class="kw-2">*</span><span class="ident">beta</span> <span class="op">-</span> <span class="ident">F::from</span>(<span class="number">14.</span> <span class="op">/</span> <span class="number">18.</span>).<span class="ident">unwrap</span>());
             <span class="kw">let</span> <span class="ident">kappa2</span> <span class="op">=</span> <span class="ident">F::from</span>(<span class="number">0.25</span>).<span class="ident">unwrap</span>()
                 <span class="op">+</span> (<span class="ident">F::from</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>() <span class="op">+</span> <span class="ident">F::from</span>(<span class="number">0.25</span>).<span class="ident">unwrap</span>()<span class="op">/</span><span class="ident">delta</span>)<span class="kw-2">*</span><span class="ident">b</span>;

             <span class="prelude-val">Ok</span>(<span class="ident">Beta</span> {
                 <span class="ident">a</span>, <span class="ident">b</span>, <span class="ident">switched_params</span>,
                 <span class="ident">algorithm</span>: <span class="ident">BetaAlgorithm::BC</span>(<span class="ident">BC</span> {
                     <span class="ident">alpha</span>, <span class="ident">beta</span>, <span class="ident">delta</span>, <span class="ident">kappa1</span>, <span class="ident">kappa2</span>,
                 })
             })
         }
     }
 }

 <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Beta</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>
 <span class="kw">where</span>
     <span class="ident">F</span>: <span class="ident">Float</span>,
     <span class="ident">Open01</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">F</span><span class="op">&gt;</span>,
 {
     <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;mut</span> <span class="ident">R</span>) -&gt; <span class="ident">F</span> {
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">w</span>;
         <span class="kw">match</span> <span class="self">self</span>.<span class="ident">algorithm</span> {
             <span class="ident">BetaAlgorithm::BB</span>(<span class="ident">algo</span>) =&gt; {
                 <span class="kw">loop</span> {
                     <span class="comment">// 1.</span>
                     <span class="kw">let</span> <span class="ident">u1</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);
                     <span class="kw">let</span> <span class="ident">u2</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);
                     <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">algo</span>.<span class="ident">beta</span> <span class="op">*</span> (<span class="ident">u1</span> <span class="op">/</span> (<span class="ident">F::one</span>() <span class="op">-</span> <span class="ident">u1</span>)).<span class="ident">ln</span>();
                     <span class="ident">w</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">a</span> <span class="op">*</span> <span class="ident">v</span>.<span class="ident">exp</span>();
                     <span class="kw">let</span> <span class="ident">z</span> <span class="op">=</span> <span class="ident">u1</span><span class="kw-2">*</span><span class="ident">u1</span> <span class="op">*</span> <span class="ident">u2</span>;
                     <span class="kw">let</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">algo</span>.<span class="ident">gamma</span> <span class="op">*</span> <span class="ident">v</span> <span class="op">-</span> <span class="ident">F::from</span>(<span class="number">4.</span>).<span class="ident">unwrap</span>().<span class="ident">ln</span>();
                     <span class="kw">let</span> <span class="ident">s</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">a</span> <span class="op">+</span> <span class="ident">r</span> <span class="op">-</span> <span class="ident">w</span>;
                     <span class="comment">// 2.</span>
                     <span class="kw">if</span> <span class="ident">s</span> <span class="op">+</span> <span class="ident">F::one</span>() <span class="op">+</span> <span class="ident">F::from</span>(<span class="number">5.</span>).<span class="ident">unwrap</span>().<span class="ident">ln</span>()
                         <span class="op">&gt;</span><span class="op">=</span> <span class="ident">F::from</span>(<span class="number">5.</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">z</span> {
                         <span class="kw">break</span>;
                     }
                     <span class="comment">// 3.</span>
                     <span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="ident">z</span>.<span class="ident">ln</span>();
                     <span class="kw">if</span> <span class="ident">s</span> <span class="op">&gt;</span><span class="op">=</span> <span class="ident">t</span> {
                         <span class="kw">break</span>;
                     }
                     <span class="comment">// 4.</span>
                     <span class="kw">if</span> <span class="op">!</span>(<span class="ident">r</span> <span class="op">+</span> <span class="ident">algo</span>.<span class="ident">alpha</span> <span class="op">*</span> (<span class="ident">algo</span>.<span class="ident">alpha</span> <span class="op">/</span> (<span class="self">self</span>.<span class="ident">b</span> <span class="op">+</span> <span class="ident">w</span>)).<span class="ident">ln</span>() <span class="op">&lt;</span> <span class="ident">t</span>) {
                         <span class="kw">break</span>;
                     }
                 }
             },
             <span class="ident">BetaAlgorithm::BC</span>(<span class="ident">algo</span>) =&gt; {
                 <span class="kw">loop</span> {
                     <span class="kw">let</span> <span class="ident">z</span>;
                     <span class="comment">// 1.</span>
                     <span class="kw">let</span> <span class="ident">u1</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);
                     <span class="kw">let</span> <span class="ident">u2</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Open01</span>);
                     <span class="kw">if</span> <span class="ident">u1</span> <span class="op">&lt;</span> <span class="ident">F::from</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>() {
                         <span class="comment">// 2.</span>
                         <span class="kw">let</span> <span class="ident">y</span> <span class="op">=</span> <span class="ident">u1</span> <span class="op">*</span> <span class="ident">u2</span>;
                         <span class="ident">z</span> <span class="op">=</span> <span class="ident">u1</span> <span class="op">*</span> <span class="ident">y</span>;
                         <span class="kw">if</span> <span class="ident">F::from</span>(<span class="number">0.25</span>).<span class="ident">unwrap</span>() <span class="op">*</span> <span class="ident">u2</span> <span class="op">+</span> <span class="ident">z</span> <span class="op">-</span> <span class="ident">y</span> <span class="op">&gt;</span><span class="op">=</span> <span class="ident">algo</span>.<span class="ident">kappa1</span> {
                             <span class="kw">continue</span>;
                         }
                     } <span class="kw">else</span> {
                         <span class="comment">// 3.</span>
                         <span class="ident">z</span> <span class="op">=</span> <span class="ident">u1</span> <span class="op">*</span> <span class="ident">u1</span> <span class="op">*</span> <span class="ident">u2</span>;
                         <span class="kw">if</span> <span class="ident">z</span> <span class="op">&lt;</span><span class="op">=</span> <span class="ident">F::from</span>(<span class="number">0.25</span>).<span class="ident">unwrap</span>() {
                             <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">algo</span>.<span class="ident">beta</span> <span class="op">*</span> (<span class="ident">u1</span> <span class="op">/</span> (<span class="ident">F::one</span>() <span class="op">-</span> <span class="ident">u1</span>)).<span class="ident">ln</span>();
                             <span class="ident">w</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">a</span> <span class="op">*</span> <span class="ident">v</span>.<span class="ident">exp</span>();
                             <span class="kw">break</span>;
                         }
                         <span class="comment">// 4.</span>
                         <span class="kw">if</span> <span class="ident">z</span> <span class="op">&gt;</span><span class="op">=</span> <span class="ident">algo</span>.<span class="ident">kappa2</span> {
                             <span class="kw">continue</span>;
                         }
                     }
                     <span class="comment">// 5.</span>
                     <span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">algo</span>.<span class="ident">beta</span> <span class="op">*</span> (<span class="ident">u1</span> <span class="op">/</span> (<span class="ident">F::one</span>() <span class="op">-</span> <span class="ident">u1</span>)).<span class="ident">ln</span>();
                     <span class="ident">w</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">a</span> <span class="op">*</span> <span class="ident">v</span>.<span class="ident">exp</span>();
                     <span class="kw">if</span> <span class="op">!</span>(<span class="ident">algo</span>.<span class="ident">alpha</span> <span class="op">*</span> ((<span class="ident">algo</span>.<span class="ident">alpha</span> <span class="op">/</span> (<span class="self">self</span>.<span class="ident">b</span> <span class="op">+</span> <span class="ident">w</span>)).<span class="ident">ln</span>() <span class="op">+</span> <span class="ident">v</span>)
                          <span class="op">-</span> <span class="ident">F::from</span>(<span class="number">4.</span>).<span class="ident">unwrap</span>().<span class="ident">ln</span>() <span class="op">&lt;</span> <span class="ident">z</span>.<span class="ident">ln</span>()) {
                         <span class="kw">break</span>;
                     };
                 }
             },
         };
         <span class="comment">// 5. for BB, 6. for BC</span>
         <span class="kw">if</span> <span class="op">!</span><span class="self">self</span>.<span class="ident">switched_params</span> {
             <span class="kw">if</span> <span class="ident">w</span> <span class="op">==</span> <span class="ident">F::infinity</span>() {
                 <span class="comment">// Assuming `b` is finite, for large `w`:</span>
                 <span class="kw">return</span> <span class="ident">F::one</span>();
             }
             <span class="ident">w</span> <span class="op">/</span> (<span class="self">self</span>.<span class="ident">b</span> <span class="op">+</span> <span class="ident">w</span>)
         } <span class="kw">else</span> {
             <span class="self">self</span>.<span class="ident">b</span> <span class="op">/</span> (<span class="self">self</span>.<span class="ident">b</span> <span class="op">+</span> <span class="ident">w</span>)
         }
     }
 }

 <span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
 <span class="kw">mod</span> <span class="ident">test</span> {
     <span class="kw">use</span> <span class="kw">super</span>::<span class="kw-2">*</span>;

     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_chi_squared_one</span>() {
         <span class="kw">let</span> <span class="ident">chi</span> <span class="op">=</span> <span class="ident">ChiSquared::new</span>(<span class="number">1.0</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">201</span>);
         <span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="ident">chi</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
         }
     }
     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_chi_squared_small</span>() {
         <span class="kw">let</span> <span class="ident">chi</span> <span class="op">=</span> <span class="ident">ChiSquared::new</span>(<span class="number">0.5</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">202</span>);
         <span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="ident">chi</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
         }
     }
     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_chi_squared_large</span>() {
         <span class="kw">let</span> <span class="ident">chi</span> <span class="op">=</span> <span class="ident">ChiSquared::new</span>(<span class="number">30.0</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">203</span>);
         <span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="ident">chi</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
         }
     }
     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="attribute">#[<span class="ident">should_panic</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_chi_squared_invalid_dof</span>() {
         <span class="ident">ChiSquared::new</span>(<span class="op">-</span><span class="number">1.0</span>).<span class="ident">unwrap</span>();
     }

     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_f</span>() {
         <span class="kw">let</span> <span class="ident">f</span> <span class="op">=</span> <span class="ident">FisherF::new</span>(<span class="number">2.0</span>, <span class="number">32.0</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">204</span>);
         <span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="ident">f</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
         }
     }

     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_t</span>() {
         <span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="ident">StudentT::new</span>(<span class="number">11.0</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">205</span>);
         <span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="ident">t</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
         }
     }

     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_beta</span>() {
         <span class="kw">let</span> <span class="ident">beta</span> <span class="op">=</span> <span class="ident">Beta::new</span>(<span class="number">1.0</span>, <span class="number">2.0</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">201</span>);
         <span class="kw">for</span> <span class="kw">_</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="ident">beta</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>);
         }
     }

     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="attribute">#[<span class="ident">should_panic</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_beta_invalid_dof</span>() {
         <span class="ident">Beta::new</span>(<span class="number">0.</span>, <span class="number">0.</span>).<span class="ident">unwrap</span>();
     }

     <span class="attribute">#[<span class="ident">test</span>]</span>
     <span class="kw">fn</span> <span class="ident">test_beta_small_param</span>() {
         <span class="kw">let</span> <span class="ident">beta</span> <span class="op">=</span> <span class="ident">Beta</span>::<span class="op">&lt;</span><span class="ident">f64</span><span class="op">&gt;</span><span class="ident">::new</span>(<span class="number">1e-3</span>, <span class="number">1e-3</span>).<span class="ident">unwrap</span>();
         <span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="ident"><span class="kw">crate</span>::test::rng</span>(<span class="number">206</span>);
         <span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="number">0</span>..<span class="number">1000</span> {
             <span class="macro">assert!</span>(<span class="op">!</span><span class="ident">beta</span>.<span class="ident">sample</span>(<span class="kw-2">&amp;mut</span> <span class="ident">rng</span>).<span class="ident">is_nan</span>(), <span class="string">&quot;failed at i={}&quot;</span>, <span class="ident">i</span>);
         }
     }
 }
 </code></pre></div>
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