| // Copyright 2018 Developers of the Rand project. |
| // Copyright 2016-2017 The Rust Project Developers. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or https://opensource.org/licenses/MIT>, 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<N> { |
| 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<N: Float> Cauchy<N> |
| where Standard: Distribution<N> |
| { |
| /// 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<Cauchy<N>, Error> { |
| if !(scale > N::from(0.0)) { |
| return Err(Error::ScaleTooSmall); |
| } |
| Ok(Cauchy { |
| median, |
| scale |
| }) |
| } |
| } |
| |
| impl<N: Float> Distribution<N> for Cauchy<N> |
| where Standard: Distribution<N> |
| { |
| fn sample<R: Rng + ?Sized>(&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(); |
| } |
| } |