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 // Copyright 2018 Developers of the Rand project. // Copyright 2016-2017 The Rust Project Developers. // // Licensed under the Apache License, Version 2.0 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! The Cauchy distribution. use rand::Rng; use crate::{Distribution, Standard}; use crate::utils::Float; /// The Cauchy distribution `Cauchy(median, scale)`. /// /// This distribution has a density function: /// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))` /// /// # Example /// /// ``` /// use rand_distr::{Cauchy, Distribution}; /// /// let cau = Cauchy::new(2.0, 5.0).unwrap(); /// let v = cau.sample(&mut rand::thread_rng()); /// println!("{} is from a Cauchy(2, 5) distribution", v); /// ``` #[derive(Clone, Copy, Debug)] pub struct Cauchy { median: N, scale: N, } /// Error type returned from `Cauchy::new`. #[derive(Clone, Copy, Debug, PartialEq, Eq)] pub enum Error { /// `scale <= 0` or `nan`. ScaleTooSmall, } impl Cauchy where Standard: Distribution { /// Construct a new `Cauchy` with the given shape parameters /// `median` the peak location and `scale` the scale factor. pub fn new(median: N, scale: N) -> Result, Error> { if !(scale > N::from(0.0)) { return Err(Error::ScaleTooSmall); } Ok(Cauchy { median, scale }) } } impl Distribution for Cauchy where Standard: Distribution { fn sample(&self, rng: &mut R) -> N { // sample from [0, 1) let x = Standard.sample(rng); // get standard cauchy random number // note that π/2 is not exactly representable, even if x=0.5 the result is finite let comp_dev = (N::pi() * x).tan(); // shift and scale according to parameters self.median + self.scale * comp_dev } } #[cfg(test)] mod test { use crate::Distribution; use super::Cauchy; fn median(mut numbers: &mut [f64]) -> f64 { sort(&mut numbers); let mid = numbers.len() / 2; numbers[mid] } fn sort(numbers: &mut [f64]) { numbers.sort_by(|a, b| a.partial_cmp(b).unwrap()); } #[test] fn test_cauchy_averages() { // NOTE: given that the variance and mean are undefined, // this test does not have any rigorous statistical meaning. let cauchy = Cauchy::new(10.0, 5.0).unwrap(); let mut rng = crate::test::rng(123); let mut numbers: [f64; 1000] = [0.0; 1000]; let mut sum = 0.0; for i in 0..1000 { numbers[i] = cauchy.sample(&mut rng); sum += numbers[i]; } let median = median(&mut numbers); println!("Cauchy median: {}", median); assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough let mean = sum / 1000.0; println!("Cauchy mean: {}", mean); // for a Cauchy distribution the mean should not converge assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough } #[test] #[should_panic] fn test_cauchy_invalid_scale_zero() { Cauchy::new(0.0, 0.0).unwrap(); } #[test] #[should_panic] fn test_cauchy_invalid_scale_neg() { Cauchy::new(0.0, -10.0).unwrap(); } }