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
|
// Copyright 2018 Developers of the Rand project.
// Copyright 2016-2017 The Rust Project Developers.
//
// 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 Cauchy distribution.
use rand::Rng;
use crate::{Distribution, Standard};
use crate::utils::Float;
/// The Cauchy distribution `Cauchy(median, scale)`.
///
/// This distribution has a density function:
/// `f(x) = 1 / (pi * scale * (1 + ((x - median) / scale)^2))`
///
/// # Example
///
/// ```
/// use rand_distr::{Cauchy, Distribution};
///
/// let cau = Cauchy::new(2.0, 5.0).unwrap();
/// let v = cau.sample(&mut rand::thread_rng());
/// println!("{} is from a Cauchy(2, 5) distribution", v);
/// ```
#[derive(Clone, Copy, Debug)]
pub struct Cauchy<N> {
median: N,
scale: N,
}
/// Error type returned from `Cauchy::new`.
#[derive(Clone, Copy, Debug, PartialEq, Eq)]
pub enum Error {
/// `scale <= 0` or `nan`.
ScaleTooSmall,
}
impl<N: Float> Cauchy<N>
where Standard: Distribution<N>
{
/// Construct a new `Cauchy` with the given shape parameters
/// `median` the peak location and `scale` the scale factor.
pub fn new(median: N, scale: N) -> Result<Cauchy<N>, Error> {
if !(scale > N::from(0.0)) {
return Err(Error::ScaleTooSmall);
}
Ok(Cauchy {
median,
scale
})
}
}
impl<N: Float> Distribution<N> for Cauchy<N>
where Standard: Distribution<N>
{
fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
// sample from [0, 1)
let x = Standard.sample(rng);
// get standard cauchy random number
// note that π/2 is not exactly representable, even if x=0.5 the result is finite
let comp_dev = (N::pi() * x).tan();
// shift and scale according to parameters
self.median + self.scale * comp_dev
}
}
#[cfg(test)]
mod test {
use crate::Distribution;
use super::Cauchy;
fn median(mut numbers: &mut [f64]) -> f64 {
sort(&mut numbers);
let mid = numbers.len() / 2;
numbers[mid]
}
fn sort(numbers: &mut [f64]) {
numbers.sort_by(|a, b| a.partial_cmp(b).unwrap());
}
#[test]
fn test_cauchy_averages() {
// NOTE: given that the variance and mean are undefined,
// this test does not have any rigorous statistical meaning.
let cauchy = Cauchy::new(10.0, 5.0).unwrap();
let mut rng = crate::test::rng(123);
let mut numbers: [f64; 1000] = [0.0; 1000];
let mut sum = 0.0;
for i in 0..1000 {
numbers[i] = cauchy.sample(&mut rng);
sum += numbers[i];
}
let median = median(&mut numbers);
println!("Cauchy median: {}", median);
assert!((median - 10.0).abs() < 0.4); // not 100% certain, but probable enough
let mean = sum / 1000.0;
println!("Cauchy mean: {}", mean);
// for a Cauchy distribution the mean should not converge
assert!((mean - 10.0).abs() > 0.4); // not 100% certain, but probable enough
}
#[test]
#[should_panic]
fn test_cauchy_invalid_scale_zero() {
Cauchy::new(0.0, 0.0).unwrap();
}
#[test]
#[should_panic]
fn test_cauchy_invalid_scale_neg() {
Cauchy::new(0.0, -10.0).unwrap();
}
}
|
