1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
// 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.

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

/// Samples floating-point numbers according to the Weibull distribution
///
/// # 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)]
#[cfg_attr(feature = "serde1", 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")]
#[cfg_attr(doc_cfg, doc(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 + core::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,
        ]);
    }
}