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``````//! The inverse Gaussian distribution `IG(μ, λ)`.

use crate::{Distribution, Standard, StandardNormal};
use core::fmt;
use num_traits::Float;
use rand::Rng;

/// Error type returned from [`InverseGaussian::new`]
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum Error {
/// `mean <= 0` or `nan`.
MeanNegativeOrNull,
/// `shape <= 0` or `nan`.
ShapeNegativeOrNull,
}

impl fmt::Display for Error {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
Error::MeanNegativeOrNull => "mean <= 0 or is NaN in inverse Gaussian distribution",
Error::ShapeNegativeOrNull => "shape <= 0 or is NaN in inverse Gaussian distribution",
})
}
}

#[cfg(feature = "std")]
impl std::error::Error for Error {}

/// The [inverse Gaussian distribution](https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution) `IG(μ, λ)`.
///
/// This is a continuous probability distribution with mean parameter `μ` (`mu`)
/// and shape parameter `λ` (`lambda`), defined for `x > 0`.
/// It is also known as the Wald distribution.
///
/// # Plot
///
/// The following plot shows the inverse Gaussian distribution
/// with various values of `μ` and `λ`.
///
/// ![Inverse Gaussian distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/inverse_gaussian.svg)
///
/// # Example
/// ```
/// use rand_distr::{InverseGaussian, Distribution};
///
/// let inv_gauss = InverseGaussian::new(1.0, 2.0).unwrap();
/// let v = inv_gauss.sample(&mut rand::thread_rng());
/// println!("{} is from a inverse Gaussian(1, 2) distribution", v);
/// ```
#[derive(Debug, Clone, Copy, PartialEq)]
#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
pub struct InverseGaussian<F>
where
F: Float,
StandardNormal: Distribution<F>,
Standard: Distribution<F>,
{
mean: F,
shape: F,
}

impl<F> InverseGaussian<F>
where
F: Float,
StandardNormal: Distribution<F>,
Standard: Distribution<F>,
{
/// Construct a new `InverseGaussian` distribution with the given mean and
/// shape.
pub fn new(mean: F, shape: F) -> Result<InverseGaussian<F>, Error> {
let zero = F::zero();
if !(mean > zero) {
return Err(Error::MeanNegativeOrNull);
}

if !(shape > zero) {
return Err(Error::ShapeNegativeOrNull);
}

Ok(Self { mean, shape })
}
}

impl<F> Distribution<F> for InverseGaussian<F>
where
F: Float,
StandardNormal: Distribution<F>,
Standard: Distribution<F>,
{
#[allow(clippy::many_single_char_names)]
fn sample<R>(&self, rng: &mut R) -> F
where
R: Rng + ?Sized,
{
let mu = self.mean;
let l = self.shape;

let v: F = rng.sample(StandardNormal);
let y = mu * v * v;

let mu_2l = mu / (F::from(2.).unwrap() * l);

let x = mu + mu_2l * (y - (F::from(4.).unwrap() * l * y + y * y).sqrt());

let u: F = rng.random();

if u <= mu / (mu + x) {
return x;
}

mu * mu / x
}
}

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn test_inverse_gaussian() {
let inv_gauss = InverseGaussian::new(1.0, 1.0).unwrap();
let mut rng = crate::test::rng(210);
for _ in 0..1000 {
inv_gauss.sample(&mut rng);
}
}

#[test]
fn test_inverse_gaussian_invalid_param() {
assert!(InverseGaussian::new(-1.0, 1.0).is_err());
assert!(InverseGaussian::new(-1.0, -1.0).is_err());
assert!(InverseGaussian::new(1.0, -1.0).is_err());
assert!(InverseGaussian::new(1.0, 1.0).is_ok());
}

#[test]
fn inverse_gaussian_distributions_can_be_compared() {
assert_eq!(
InverseGaussian::new(1.0, 2.0),
InverseGaussian::new(1.0, 2.0)
);
}
}
``````