Struct BetaDistribution 

pub struct BetaDistribution {
    pub alpha: f64,
    pub beta: f64,
}

Beta distribution on [0, 1].

Mathematical Definition

• PDF: f(x) = x^(α−1) (1−x)^(β−1) / B(α, β)
• CDF: F(x) = I_x(α, β) (regularized incomplete beta)
• Mean: α / (α + β)
• Variance: αβ / ((α+β)²(α+β+1))

Examples

use u_numflow::distributions::BetaDistribution;

let beta = BetaDistribution::new(2.0, 5.0).unwrap();
assert!((beta.mean() - 2.0 / 7.0).abs() < 1e-10);
assert!(beta.pdf(0.3) > 0.0);
assert!((beta.cdf(0.0)).abs() < 1e-10);
assert!((beta.cdf(1.0) - 1.0).abs() < 1e-10);

References

Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995). Continuous Univariate Distributions, Vol. 2, Chapter 25.

Fields

alpha: f64

Shape parameter α > 0.

beta: f64

Shape parameter β > 0.

Implementations

impl BetaDistribution

pub fn new(alpha: f64, beta: f64) -> Result<Self, DistributionError>

Creates a new Beta distribution with shape parameters α and β.

Errors

Returns DistributionError if α ≤ 0 or β ≤ 0.

pub fn mean(&self) -> f64

Returns the mean: α / (α + β).

pub fn variance(&self) -> f64

Returns the variance: αβ / ((α+β)²(α+β+1)).

pub fn mode(&self) -> Option<f64>

Returns the mode.

Defined when α > 1 and β > 1: mode = (α−1)/(α+β−2). Returns None for other parameter combinations (bimodal or boundary modes).

pub fn pdf(&self, x: f64) -> f64

Evaluates the PDF at x.

pub fn cdf(&self, x: f64) -> f64

Evaluates the CDF at x: F(x) = I_x(α, β).

pub fn quantile(&self, p: f64) -> Option<f64>

Evaluates the quantile (inverse CDF) at probability p ∈ [0, 1].

Uses Newton-Raphson iteration with an initial approximation from the normal approximation to the beta distribution.

Trait Implementations

impl Clone for BetaDistribution

fn clone(&self) -> BetaDistribution

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for BetaDistribution

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.