rand_distr/
normal_inverse_gaussian.rs

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

rand_distr/
normal_inverse_gaussian.rs
