Struct ProbabilityMeasure 

pub struct ProbabilityMeasure {
    pub density: Box<dyn Fn(&[f64]) -> f64>,
    pub domain: MeasurableSet,
    pub n_samples: usize,
}

A probability measure on ℝⁿ with density function.

P(A) = ∫_A f(x) dx where ∫ f dx = 1 (normalization).

Supports numerical expectation and variance via Monte Carlo estimation.

Fields

density: Box<dyn Fn(&[f64]) -> f64>

Probability density function f(x) ≥ 0.

domain: MeasurableSet

Domain of the density (support box).

n_samples: usize

Number of Monte Carlo samples for numerical computations.

Implementations

impl ProbabilityMeasure

pub fn new( density: impl Fn(&[f64]) -> f64 + 'static, domain: MeasurableSet, n_samples: usize, ) -> Self

Create a probability measure from a density and domain.

pub fn probability(&self, set: &MeasurableSet) -> f64

Estimate P(A) via Monte Carlo integration.

Samples uniformly from the domain and averages the density over A.

pub fn total_mass(&self) -> f64

Estimate the total mass (should be ≈ 1 for a true probability measure).

pub fn expectation(&self, g: &dyn Fn(&[f64]) -> f64) -> f64

Estimate the expectation E[g(X)] of a function g under this measure.

pub fn variance(&self, g: &dyn Fn(&[f64]) -> f64) -> f64

Estimate Var[g(X)] = E[g(X)²] − (E[g(X)])².

pub fn entropy(&self) -> f64

Estimate the entropy H = -∫ f ln(f) dx via Monte Carlo.