numeris 0.5.2

Pure-Rust numerical algorithms library — high performance with SIMD support while also supporting no-std for embedded and WASM targets.
Documentation 
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

use crate::FloatScalar;
use crate::special::{lbeta, betainc};
use super::{ContinuousDistribution, StatsError, quantile_newton};

/// Beta distribution with shape parameters α and β on [0, 1].
///
/// f(x) = x^{α−1} (1−x)^{β−1} / B(α, β) for 0 ≤ x ≤ 1.
///
/// # Example
///
/// ```
/// use numeris::stats::{Beta, ContinuousDistribution};
///
/// let b = Beta::new(2.0_f64, 5.0).unwrap();
/// assert!((b.mean() - 2.0/7.0).abs() < 1e-14);
/// ```
#[derive(Debug, Clone, Copy)]
pub struct Beta<T> {
    alpha: T,
    beta: T,
}

impl<T: FloatScalar> Beta<T> {
    /// Create a Beta distribution with shape parameters `alpha` and `beta`.
    /// Requires both > 0.
    pub fn new(alpha: T, beta: T) -> Result<Self, StatsError> {
        if alpha <= T::zero() || beta <= T::zero() {
            return Err(StatsError::InvalidParameter);
        }
        Ok(Self { alpha, beta })
    }
}

impl<T: FloatScalar> Beta<T> {
    /// Draw a random sample from this distribution.
    ///
    /// Samples X ~ Gamma(alpha, 1), Y ~ Gamma(beta, 1), returns X / (X + Y).
    pub fn sample(&self, rng: &mut super::Rng) -> T {
        let x = rng.next_gamma(self.alpha);
        let y = rng.next_gamma(self.beta);
        x / (x + y)
    }

    /// Fill a fixed-size array with independent samples.
    pub fn sample_array<const K: usize>(&self, rng: &mut super::Rng) -> [T; K] {
        let mut out = [T::zero(); K];
        for v in out.iter_mut() {
            *v = self.sample(rng);
        }
        out
    }
}

impl<T: FloatScalar> ContinuousDistribution<T> for Beta<T> {
    fn pdf(&self, x: T) -> T {
        if x < T::zero() || x > T::one() {
            return T::zero();
        }
        self.ln_pdf(x).exp()
    }

    fn ln_pdf(&self, x: T) -> T {
        if x < T::zero() || x > T::one() {
            return T::neg_infinity();
        }
        let one = T::one();
        (self.alpha - one) * x.ln() + (self.beta - one) * (one - x).ln()
            - lbeta(self.alpha, self.beta)
    }

    fn cdf(&self, x: T) -> T {
        if x <= T::zero() {
            return T::zero();
        }
        if x >= T::one() {
            return T::one();
        }
        betainc(self.alpha, self.beta, x).unwrap_or(T::nan())
    }

    fn quantile(&self, p: T) -> T {
        let x0 = self.mean();
        let eps = T::epsilon();
        quantile_newton(
            |x| self.cdf(x),
            |x| self.pdf(x),
            p,
            x0,
            eps,
            T::one() - eps,
        )
    }

    fn mean(&self) -> T {
        self.alpha / (self.alpha + self.beta)
    }

    fn variance(&self) -> T {
        let ab = self.alpha + self.beta;
        self.alpha * self.beta / (ab * ab * (ab + T::one()))
    }
}