Struct PoissonProcess 

pub struct PoissonProcess {
    pub lambda: f64,
}

Poisson process simulator and summary statistics.

A Poisson process N(t) with rate λ: inter-arrival times are Exp(λ).

Fields

lambda: f64

Arrival rate λ > 0.

Implementations

impl PoissonProcess

pub fn new(lambda: f64) -> Self

Creates a PoissonProcess with rate λ.

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

Expected number of arrivals in [0, t]: E[N(t)] = λ t.

pub fn count_pmf(&self, t: f64, k: u32) -> f64

PMF of N(t): P(N(t) = k) = (λt)^k e^{-λt} / k!

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

Variance of N(t): Var[N(t)] = λ t.

pub fn simulate_arrivals(&self, t_max: f64, lcg: &mut Lcg) -> Vec<f64>

Generates inter-arrival times up to total time t_max using an LCG. Returns the vector of arrival times within [0, t_max].

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

Compound Poisson process: E[Σ Y_i] = λ t E[Y] for i.i.d. jumps Y.