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``````// Copyright 2018 Developers of the Rand project.
//
// option. This file may not be copied, modified, or distributed
// except according to those terms.

//! The Weibull distribution `Weibull(λ, k)`

use crate::{Distribution, OpenClosed01};
use core::fmt;
use num_traits::Float;
use rand::Rng;

/// The [Weibull distribution](https://en.wikipedia.org/wiki/Weibull_distribution) `Weibull(λ, k)`.
///
/// This is a family of continuous probability distributions with
/// scale parameter `λ` (`lambda`) and shape parameter `k`. It is used
/// to model reliability data, life data, and accelerated life testing data.
///
/// # Plot
///
/// The following plot shows the Weibull distribution with various values of `λ` and `k`.
///
/// ![Weibull distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/weibull.svg)
///
/// # Example
/// ```
/// use rand::prelude::*;
/// use rand_distr::Weibull;
///
/// let val: f64 = thread_rng().sample(Weibull::new(1., 10.).unwrap());
/// println!("{}", val);
/// ```
#[derive(Clone, Copy, Debug, PartialEq)]
#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
pub struct Weibull<F>
where
F: Float,
OpenClosed01: Distribution<F>,
{
inv_shape: F,
scale: F,
}

/// Error type returned from [`Weibull::new`].
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `scale <= 0` or `nan`.
ScaleTooSmall,
/// `shape <= 0` or `nan`.
ShapeTooSmall,
}

impl fmt::Display for Error {
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
f.write_str(match self {
Error::ScaleTooSmall => "scale is not positive in Weibull distribution",
Error::ShapeTooSmall => "shape is not positive in Weibull distribution",
})
}
}

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

impl<F> Weibull<F>
where
F: Float,
OpenClosed01: Distribution<F>,
{
/// Construct a new `Weibull` distribution with given `scale` and `shape`.
pub fn new(scale: F, shape: F) -> Result<Weibull<F>, Error> {
if !(scale > F::zero()) {
return Err(Error::ScaleTooSmall);
}
if !(shape > F::zero()) {
return Err(Error::ShapeTooSmall);
}
Ok(Weibull {
inv_shape: F::from(1.).unwrap() / shape,
scale,
})
}
}

impl<F> Distribution<F> for Weibull<F>
where
F: Float,
OpenClosed01: Distribution<F>,
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F {
let x: F = rng.sample(OpenClosed01);
self.scale * (-x.ln()).powf(self.inv_shape)
}
}

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

#[test]
#[should_panic]
fn invalid() {
Weibull::new(0., 0.).unwrap();
}

#[test]
fn sample() {
let scale = 1.0;
let shape = 2.0;
let d = Weibull::new(scale, shape).unwrap();
let mut rng = crate::test::rng(1);
for _ in 0..1000 {
let r = d.sample(&mut rng);
assert!(r >= 0.);
}
}

#[test]
fn value_stability() {
fn test_samples<F: Float + fmt::Debug, D: Distribution<F>>(
distr: D,
zero: F,
expected: &[F],
) {
let mut rng = crate::test::rng(213);
let mut buf = [zero; 4];
for x in &mut buf {
*x = rng.sample(&distr);
}
assert_eq!(buf, expected);
}

test_samples(
Weibull::new(1.0, 1.0).unwrap(),
0f32,
&[0.041495778, 0.7531094, 1.4189332, 0.38386202],
);
test_samples(
Weibull::new(2.0, 0.5).unwrap(),
0f64,
&[
1.1343478702739669,
0.29470010050655226,
0.7556151370284702,
7.877212340241561,
],
);
}

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