Distribution

 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

use crate::algebra::abstr::Real;
use std::iter;

pub trait Distribution<T>
where
    T: Real,
{
    fn random(&self) -> T;

    fn random_sequence(&self, size: u32) -> Vec<T> {
        let mut v: Vec<T> = Vec::new();
        v.extend(iter::repeat_with(&|| self.random()).take(size as usize));

        v
    }
}

/// Continuous distribution
pub trait Continuous<T>
where
    T: Real,
{
    /// Probability density function
    ///
    /// # Arguments
    ///
    /// *`x`:
    fn pdf(&self, x: T) -> T;

    /// Cumulative distribution function
    ///
    /// # Arguments
    ///
    /// *`x`:
    fn cdf(&self, x: T) -> T;

    /// Quantile function, inverse cdf
    fn quantile(&self, p: T) -> T;

    /// Mean
    fn mean(&self) -> T;

    /// Variance
    fn variance(&self) -> T;

    /// Skewness is a measure of the asymmetry of the probability distribution
    /// of a real-valued random variable about its mean
    fn skewness(&self) -> T;

    /// Median is the value separating the higher half from the lower half of a
    /// probability distribution.
    fn median(&self) -> T;

    ///
    fn entropy(&self) -> T;
}

/// Discrete distribution
pub trait Discrete<T, A, B> {
    /// Probability mass function
    ///
    /// # Arguments
    ///
    /// *`x`:
    fn pmf(&self, x: A) -> T;

    ///Cumulative distribution function
    ///
    /// # Arguments
    ///
    /// * `x`:
    fn cdf(&self, x: B) -> T;

    /// Mean
    fn mean(&self) -> T;

    /// Variance
    fn variance(&self) -> T;
}

 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

use crate::algebra::abstr::Real;
use std::iter;

pub trait Distribution<T>
where
    T: Real,
{
    fn random(&self) -> T;

    fn random_sequence(&self, size: u32) -> Vec<T> {
        let mut v: Vec<T> = Vec::new();
        v.extend(iter::repeat_with(&|| self.random()).take(size as usize));

        v
    }
}

/// Continuous distribution
pub trait Continuous<T>
where
    T: Real,
{
    /// Probability density function
    ///
    /// # Arguments
    ///
    /// *`x`:
    fn pdf(&self, x: T) -> T;

    /// Cumulative distribution function
    ///
    /// # Arguments
    ///
    /// *`x`:
    fn cdf(&self, x: T) -> T;

    /// Quantile function, inverse cdf
    fn quantile(&self, p: T) -> T;

    /// Mean
    fn mean(&self) -> T;

    /// Variance
    fn variance(&self) -> T;

    /// Skewness is a measure of the asymmetry of the probability distribution
    /// of a real-valued random variable about its mean
    fn skewness(&self) -> T;

    /// Median is the value separating the higher half from the lower half of a
    /// probability distribution.
    fn median(&self) -> T;

    ///
    fn entropy(&self) -> T;
}

/// Discrete distribution
pub trait Discrete<T, A, B> {
    /// Probability mass function
    ///
    /// # Arguments
    ///
    /// *`x`:
    fn pmf(&self, x: A) -> T;

    ///Cumulative distribution function
    ///
    /// # Arguments
    ///
    /// * `x`:
    fn cdf(&self, x: B) -> T;

    /// Mean
    fn mean(&self) -> T;

    /// Variance
    fn variance(&self) -> T;
}