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 PERT distribution.
use rand::Rng;
use crate::{Distribution, Beta, StandardNormal, Exp1, Open01};
use crate::utils::Float;
/// The PERT distribution.
///
/// Similar to the [`Triangular`] distribution, the PERT distribution is
/// parameterised by a range and a mode within that range. Unlike the
/// [`Triangular`] distribution, the probability density function of the PERT
/// distribution is smooth, with a configurable weighting around the mode.
///
/// # Example
///
/// ```rust
/// use rand_distr::{Pert, Distribution};
///
/// let d = Pert::new(0., 5., 2.5).unwrap();
/// let v = d.sample(&mut rand::thread_rng());
/// println!("{} is from a PERT distribution", v);
/// ```
///
/// [`Triangular`]: crate::Triangular
#[derive(Clone, Copy, Debug)]
pub struct Pert<N> {
min: N,
range: N,
beta: Beta<N>,
}
/// Error type returned from [`Pert`] constructors.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum PertError {
/// `max < min` or `min` or `max` is NaN.
RangeTooSmall,
/// `mode < min` or `mode > max` or `mode` is NaN.
ModeRange,
/// `shape < 0` or `shape` is NaN
ShapeTooSmall,
}
impl<N: Float> Pert<N>
where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
{
/// Set up the PERT distribution with defined `min`, `max` and `mode`.
///
/// This is equivalent to calling `Pert::new_shape` with `shape == 4.0`.
#[inline]
pub fn new(min: N, max: N, mode: N) -> Result<Pert<N>, PertError> {
Pert::new_with_shape(min, max, mode, N::from(4.))
}
/// Set up the PERT distribution with defined `min`, `max`, `mode` and
/// `shape`.
pub fn new_with_shape(min: N, max: N, mode: N, shape: N) -> Result<Pert<N>, PertError> {
if !(max > min) {
return Err(PertError::RangeTooSmall);
}
if !(mode >= min && max >= mode) {
return Err(PertError::ModeRange);
}
if !(shape >= N::from(0.)) {
return Err(PertError::ShapeTooSmall);
}
let range = max - min;
let mu = (min + max + shape * mode) / (shape + N::from(2.));
let v = if mu == mode {
shape * N::from(0.5) + N::from(1.)
} else {
(mu - min) * (N::from(2.) * mode - min - max)
/ ((mode - mu) * (max - min))
};
let w = v * (max - mu) / (mu - min);
let beta = Beta::new(v, w).map_err(|_| PertError::RangeTooSmall)?;
Ok(Pert{ min, range, beta })
}
}
impl<N: Float> Distribution<N> for Pert<N>
where StandardNormal: Distribution<N>, Exp1: Distribution<N>, Open01: Distribution<N>
{
#[inline]
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
self.beta.sample(rng) * self.range + self.min
}
}
#[cfg(test)]
mod test {
use std::f64;
use super::*;
#[test]
fn test_pert() {
for &(min, max, mode) in &[
(-1., 1., 0.),
(1., 2., 1.),
(5., 25., 25.),
] {
let _distr = Pert::new(min, max, mode).unwrap();
// TODO: test correctness
}
for &(min, max, mode) in &[
(-1., 1., 2.),
(-1., 1., -2.),
(2., 1., 1.),
] {
assert!(Pert::new(min, max, mode).is_err());
}
}
#[test]
fn value_stability() {
let rng = crate::test::rng(860);
let distr = Pert::new(2., 10., 3.).unwrap(); // mean = 4, var = 12/7
let seq = distr.sample_iter(rng).take(5).collect::<Vec<f64>>();
println!("seq: {:?}", seq);
let expected = vec![4.631484136029422, 3.307201472321789,
3.29995019556348, 3.66835483991721, 3.514246139933899];
assert!(seq == expected);
}
}
|
