Struct GammaDistribution 

pub struct GammaDistribution { /* private fields */ }

Gamma distribution with shape α and rate β (or equivalently scale θ = 1/β).

Uses the (shape, rate) parametrization: X ~ Gamma(α, β).

PDF

f(x) = β^α / Γ(α) · x^(α−1) · exp(−βx) for x > 0

Examples

use u_numflow::distributions::GammaDistribution;

let g = GammaDistribution::new(2.0, 1.0).unwrap();
assert!((g.mean() - 2.0).abs() < 1e-10);
assert!((g.variance() - 2.0).abs() < 1e-10);

Reference

Johnson, N.L., Kotz, S. & Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. 1, 2nd ed. Wiley.

Implementations

impl GammaDistribution

pub fn new(shape: f64, rate: f64) -> Result<Self, DistributionError>

Creates a Gamma(α, β) distribution with shape α and rate β.

Returns an error if α ≤ 0, β ≤ 0, or either is not finite.

pub fn from_shape_scale( shape: f64, scale: f64, ) -> Result<Self, DistributionError>

Creates a Gamma distribution from shape and scale θ = 1/β.

pub fn shape(&self) -> f64

Shape parameter α.

pub fn rate(&self) -> f64

Rate parameter β.

pub fn scale(&self) -> f64

Scale parameter θ = 1/β.

pub fn mean(&self) -> f64

Mean = α/β.

pub fn variance(&self) -> f64

Variance = α/β².

pub fn mode(&self) -> f64

Mode = (α−1)/β for α ≥ 1, 0 for α < 1.

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

PDF: f(x) = β^α / Γ(α) · x^(α−1) · exp(−βx) for x > 0.

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

CDF: F(x) = γ(α, βx) / Γ(α) = regularized lower incomplete gamma.

Uses series expansion for small x or continued fraction for large x.

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

Quantile (inverse CDF) via Newton-Raphson iteration.

Returns None if p is not in [0, 1].

Trait Implementations

impl Clone for GammaDistribution

fn clone(&self) -> GammaDistribution

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for GammaDistribution

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

Formats the value using the given formatter.

impl Copy for GammaDistribution