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
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
use crate::{
algebra::abstr::Real,
statistics::distrib::{Continuous, Distribution},
};
use rand::{rngs::ThreadRng, Rng};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
use std::clone::Clone;
/// Uniform distribution
///
/// Fore more information:
/// <https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)>
///
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Copy, Debug)]
pub struct Uniform<T> {
a: T,
b: T,
}
impl<T> Uniform<T>
where
T: Real,
{
/// Uniform distribution
///
/// # Arguments
///
/// -\inf < a < b < \inf
///
/// a: lower bound
/// b: upper bound
///
/// a < b
///
/// # Panic
///
/// a >= b
pub fn new(a: T, b: T) -> Uniform<T> {
if a >= b {
panic!();
}
Uniform { a, b }
}
}
impl<T> Distribution<T> for Uniform<T>
where
T: Real,
{
fn random(&self) -> T {
let mut rng: ThreadRng = rand::rng();
T::from_f64(rng.random_range(self.a.to_f64()..self.b.to_f64()))
}
}
impl<T> Continuous<T> for Uniform<T>
where
T: Real,
{
/// Probability density function
///
/// # Arguments
///
/// x:
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let distrib: Uniform<f64> = Uniform::new(-0.1, 0.3);
/// let x: f64 = 5.0;
/// let p: f64 = distrib.pdf(x);
/// ```
fn pdf(&self, x: T) -> T {
if self.a <= x && x <= self.b {
T::one() / (self.b - self.a)
} else {
T::zero()
}
}
/// Cumulative distribution function
///
/// # Arguments
///
/// * `x`
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let distrib: Uniform<f64> = Uniform::new(0.0, 0.5);
/// let x: f64 = 0.3;
/// let p: f64 = distrib.cdf(x);
/// ```
fn cdf(&self, x: T) -> T {
if x < self.a {
T::zero()
} else if x > self.b {
T::one()
} else {
(x - self.a) / (self.b - self.a)
}
}
/// Quantile function or inverse cdf
///
/// # Arguments
///
/// * `q`: quantile 0 <= q <= 1
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let distrib: Uniform<f64> = Uniform::new(0.0, 0.5);
/// let q: f64 = 0.3;
/// let x: f64 = distrib.quantile(q);
/// ```
fn quantile(&self, q: T) -> T {
if q > T::one() || q < T::zero() {
panic!("Quantile q is out of bounds");
}
q * (self.b - self.a) + self.a
}
/// Mean
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let a: f64 = 0.2;
/// let b: f64 = 0.5;
///
/// let distrib: Uniform<f64> = Uniform::new(a, b);
/// let mean: f64 = distrib.mean();
/// assert_eq!((a + b) / 2.0, mean);
/// ```
fn mean(&self) -> T {
(self.a + self.b) / T::from_f64(2.0)
}
/// Variance
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let distrib: Uniform<f64> = Uniform::new(0.2, 0.5);
/// let var: f64 = distrib.variance();
/// ```
fn variance(&self) -> T {
(self.b - self.a) * (self.b - self.a) / T::from_f64(12.0)
}
/// Skewness
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let distrib: Uniform<f64> = Uniform::new(0.2, 0.5);
/// let skewness: f64 = distrib.skewness();
/// assert_eq!(0.0, skewness);
/// ```
fn skewness(&self) -> T {
T::zero()
}
/// Median
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let a: f64 = 0.2;
/// let b: f64 = 0.5;
///
/// let distrib: Uniform<f64> = Uniform::new(a, b);
/// let median: f64 = distrib.median();
/// assert_eq!((a + b) / 2.0, median);
/// ```
fn median(&self) -> T {
self.mean()
}
/// Entropy
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, Uniform};
///
/// let a: f64 = 0.2;
/// let b: f64 = 0.5;
///
/// let distrib: Uniform<f64> = Uniform::new(a, b);
/// let entropy: f64 = distrib.entropy();
/// assert_eq!((b - a).ln(), entropy);
/// ```
fn entropy(&self) -> T {
(self.b - self.a).ln()
}
}