Struct NegativeBinomial 

pub struct NegativeBinomial { /* private fields */ }

Negative binomial claim counts in the actuarial parameterization of Klugman, Panjer & Willmot: mean r β, variance r β (1 + β).

SciPy’s nbinom(n=r, p=1/(1+β)) and R’s dnbinom(size=r, prob=1/(1+β)) are the same distribution.

use prospicio_prob::{Counting, NegativeBinomial};

let n = NegativeBinomial::from_mean_variance(10.0, 30.0).unwrap();
assert!((n.mean() - 10.0).abs() < 1e-12);
assert!((n.variance() - 30.0).abs() < 1e-12);

Implementations

impl NegativeBinomial

pub fn new(r: f64, beta: f64) -> Result<Self>

Negative binomial with shape r and scale beta; both must be finite and positive.

pub fn from_mean_variance(mean: f64, variance: f64) -> Result<Self>

The negative binomial with this mean and variance; the variance must exceed the mean (over-dispersion).

pub fn r(&self) -> f64

Shape r.

pub fn beta(&self) -> f64

Scale β.

Trait Implementations

impl Clone for NegativeBinomial

fn clone(&self) -> NegativeBinomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for NegativeBinomial

impl Counting for NegativeBinomial

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

(1 - beta (z - 1))^(-r).

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_complex(&self, (re, im): (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.

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.

impl Debug for NegativeBinomial

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

Formats the value using the given formatter.

impl PartialEq for NegativeBinomial

fn eq(&self, other: &NegativeBinomial) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for NegativeBinomial