rand_distr/
weibull.rs

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// Copyright 2018 Developers of the Rand project.
//
// 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 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.
///
/// # Density function
///
/// `f(x; λ, k) = (k / λ) * (x / λ)^(k - 1) * exp(-(x / λ)^k)` for `x >= 0`.
///
/// # 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 = rand::rng().sample(Weibull::new(1., 10.).unwrap());
/// println!("{}", val);
/// ```
///
/// # Numerics
///
/// For small `k` like `< 0.005`, even with `f64` a significant number of samples will be so small that they underflow to `0.0`
/// or so big they overflow to `inf`. This is a limitation of the floating point representation and not specific to this implementation.
#[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));
    }
}