Struct GaussianDistribution 

pub struct GaussianDistribution {
    pub mu: f64,
    pub sigma: f64,
}

Normal (Gaussian) distribution with mean μ and standard deviation σ.

Fields

mu: f64

Mean.

sigma: f64

Standard deviation (must be > 0).

Implementations

impl GaussianDistribution

pub fn new(mu: f64, sigma: f64) -> Self

Creates a GaussianDistribution.

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

Probability density function f(x; μ, σ).

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

Approximates the CDF Φ((x-μ)/σ) using the Abramowitz & Stegun rational approximation (maximum error 7.5 × 10⁻⁸).

pub fn sample_box_muller(&self, u1: f64, u2: f64) -> f64

Draws a sample using the Box–Muller transform given two uniform inputs.

pub fn mgf(&self, t: f64) -> f64

Returns the moment generating function M_X(t) = exp(μt + σ²t²/2).

pub fn standard_moment(k: u32) -> f64

Returns the k-th central moment of the standard normal distribution (μ=0, σ=1). Even moments: (k-1)!! = 1·3·5·…·(k-1). Odd moments: 0.