Trait Counting 

pub trait Counting {
    // Required methods
    fn pmf(&self, k: u64) -> f64;
    fn mean(&self) -> f64;
    fn variance(&self) -> f64;
    fn panjer_ab(&self) -> (f64, f64);
    fn pgf(&self, z: f64) -> f64;
    fn pgf_complex(&self, z: (f64, f64)) -> (f64, f64);

    // Provided methods
    fn cdf(&self, k: u64) -> f64 { ... }
    fn quantile(&self, p: f64) -> Result<u64> { ... }
    fn sample(&self, rng: &mut StreamRng, n: usize) -> Vec<u64> { ... }
}

A distribution of claim counts in the (a, b, 0) class.

Required Methods

fn pmf(&self, k: u64) -> f64

P(N = k).

fn mean(&self) -> f64

E[N].

fn variance(&self) -> f64

Var[N].

fn panjer_ab(&self) -> (f64, f64)

(a, b) with p_k = (a + b / k) p_{k-1} for k ≥ 1.

fn pgf(&self, z: f64) -> f64

Probability generating function E[z^N] for 0 ≤ z ≤ 1. Panjer’s recursion starts from P(S = 0) = pgf(f_0).

fn pgf_complex(&self, z: (f64, f64)) -> (f64, f64)

The pgf at a complex z = (re, im) with |z| ≤ 1, as (re, im). FFT aggregation applies it to the transform of the severity grid.

Provided Methods

fn cdf(&self, k: u64) -> f64

P(N ≤ k).

fn quantile(&self, p: f64) -> Result<u64>

Smallest k with P(N ≤ k) ≥ p. p = 1 gives u64::MAX.

fn sample(&self, rng: &mut StreamRng, n: usize) -> Vec<u64>

n counts from stream rng, by inverse transform.

Each draw walks the pmf from 0, so the cost grows with the mean; fine for the claim counts of a year, slow for means in the hundreds of thousands.

Dyn Compatibility

This trait is dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety".

Implementations on Foreign Types

impl<T: Counting + ?Sized> Counting for Box<T>

fn pmf(&self, k: u64) -> f64

fn mean(&self) -> f64

fn variance(&self) -> f64

fn panjer_ab(&self) -> (f64, f64)

fn pgf(&self, z: f64) -> f64

fn pgf_complex(&self, z: (f64, f64)) -> (f64, f64)

fn cdf(&self, k: u64) -> f64

fn quantile(&self, p: f64) -> Result<u64>

fn sample(&self, rng: &mut StreamRng, n: usize) -> Vec<u64>

Implementors

impl Counting for Binomial

impl Counting for NegativeBinomial

impl Counting for PanjerClass

impl Counting for Poisson