rand_distr/
inverse_gaussian.rs

1//! The inverse Gaussian distribution `IG(μ, λ)`.
2
3use crate::{Distribution, StandardNormal, StandardUniform};
4use core::fmt;
5use num_traits::Float;
6use rand::Rng;
7
8/// Error type returned from [`InverseGaussian::new`]
9#[derive(Debug, Clone, Copy, PartialEq, Eq)]
10pub enum Error {
11    /// `mean <= 0` or `nan`.
12    MeanNegativeOrNull,
13    /// `shape <= 0` or `nan`.
14    ShapeNegativeOrNull,
15}
16
17impl fmt::Display for Error {
18    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
19        f.write_str(match self {
20            Error::MeanNegativeOrNull => "mean <= 0 or is NaN in inverse Gaussian distribution",
21            Error::ShapeNegativeOrNull => "shape <= 0 or is NaN in inverse Gaussian distribution",
22        })
23    }
24}
25
26#[cfg(feature = "std")]
27impl std::error::Error for Error {}
28
29/// The [inverse Gaussian distribution](https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution) `IG(μ, λ)`.
30///
31/// This is a continuous probability distribution with mean parameter `μ` (`mu`)
32/// and shape parameter `λ` (`lambda`), defined for `x > 0`.
33/// It is also known as the Wald distribution.
34///
35/// # Plot
36///
37/// The following plot shows the inverse Gaussian distribution
38/// with various values of `μ` and `λ`.
39///
40/// ![Inverse Gaussian distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/inverse_gaussian.svg)
41///
42/// # Example
43/// ```
44/// use rand_distr::{InverseGaussian, Distribution};
45///
46/// let inv_gauss = InverseGaussian::new(1.0, 2.0).unwrap();
47/// let v = inv_gauss.sample(&mut rand::rng());
48/// println!("{} is from a inverse Gaussian(1, 2) distribution", v);
49/// ```
50#[derive(Debug, Clone, Copy, PartialEq)]
51#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
52pub struct InverseGaussian<F>
53where
54    F: Float,
55    StandardNormal: Distribution<F>,
56    StandardUniform: Distribution<F>,
57{
58    mean: F,
59    shape: F,
60}
61
62impl<F> InverseGaussian<F>
63where
64    F: Float,
65    StandardNormal: Distribution<F>,
66    StandardUniform: Distribution<F>,
67{
68    /// Construct a new `InverseGaussian` distribution with the given mean and
69    /// shape.
70    pub fn new(mean: F, shape: F) -> Result<InverseGaussian<F>, Error> {
71        let zero = F::zero();
72        if !(mean > zero) {
73            return Err(Error::MeanNegativeOrNull);
74        }
75
76        if !(shape > zero) {
77            return Err(Error::ShapeNegativeOrNull);
78        }
79
80        Ok(Self { mean, shape })
81    }
82}
83
84impl<F> Distribution<F> for InverseGaussian<F>
85where
86    F: Float,
87    StandardNormal: Distribution<F>,
88    StandardUniform: Distribution<F>,
89{
90    #[allow(clippy::many_single_char_names)]
91    fn sample<R>(&self, rng: &mut R) -> F
92    where
93        R: Rng + ?Sized,
94    {
95        let mu = self.mean;
96        let l = self.shape;
97
98        let v: F = rng.sample(StandardNormal);
99        let y = mu * v * v;
100
101        let mu_2l = mu / (F::from(2.).unwrap() * l);
102
103        let x = mu + mu_2l * (y - (F::from(4.).unwrap() * l * y + y * y).sqrt());
104
105        let u: F = rng.random();
106
107        if u <= mu / (mu + x) {
108            return x;
109        }
110
111        mu * mu / x
112    }
113}
114
115#[cfg(test)]
116mod tests {
117    use super::*;
118
119    #[test]
120    fn test_inverse_gaussian() {
121        let inv_gauss = InverseGaussian::new(1.0, 1.0).unwrap();
122        let mut rng = crate::test::rng(210);
123        for _ in 0..1000 {
124            inv_gauss.sample(&mut rng);
125        }
126    }
127
128    #[test]
129    fn test_inverse_gaussian_invalid_param() {
130        assert!(InverseGaussian::new(-1.0, 1.0).is_err());
131        assert!(InverseGaussian::new(-1.0, -1.0).is_err());
132        assert!(InverseGaussian::new(1.0, -1.0).is_err());
133        assert!(InverseGaussian::new(1.0, 1.0).is_ok());
134    }
135
136    #[test]
137    fn inverse_gaussian_distributions_can_be_compared() {
138        assert_eq!(
139            InverseGaussian::new(1.0, 2.0),
140            InverseGaussian::new(1.0, 2.0)
141        );
142    }
143}
rand_distr/inverse_gaussian.rs

rand_distr/
inverse_gaussian.rs
