Struct NegativeBinomial 

pub struct NegativeBinomial { /* private fields */ }

Negative binomial distribution with target successes r and success probability p.

Models the “number of failures before the r-th success” in a sequence of independent Bernoulli trials. The CDF reduces to the incomplete Β: Pr[F ≤ s] = Iₚ(r, s + 1).

Notes

Entropy is not implemented.

Example

use cdflib::NegativeBinomial;
use cdflib::traits::{Discrete, DiscreteCdf};

let nb = NegativeBinomial::new(5, 0.5);

// Probability of 3 or fewer failures before 5th success
let cdf = nb.cdf(3);

// Compute success probability given Pr[F ≤ 5] = 0.9 and r = 10
let pr = NegativeBinomial::search_pr(0.9, 0.1, 10, 5).unwrap();

Implementations

impl NegativeBinomial

pub fn new(r: u64, pr: f64) -> Self

Construct a NegBin(r, pr) distribution with target successes r ≥ 1 and success probability pr ∈ (0 . . 1].

Panics

Panics if either argument is invalid; use try_new for a fallible variant.

pub fn try_new(r: u64, pr: f64) -> Result<Self, NegativeBinomialError>

Fallible counterpart of new returning a NegativeBinomialError instead of panicking.

pub const fn r(&self) -> u64

Returns the target number of successes r.

pub const fn pr(&self) -> f64

Returns the success probability pr.

pub fn search_r( p: f64, q: f64, pr: f64, s: u64, ) -> Result<f64, NegativeBinomialError>

Returns the target number of successes r satisfying Pr[F ≤ s] = p given the success probability.

Mirrors CDFLIB’s cdfnbn with which = 3. Caller passes both p and q = 1 − p; consistency is enforced within 3ε.

pub fn search_pr( p: f64, q: f64, r: u64, s: u64, ) -> Result<f64, NegativeBinomialError>

Returns the success probability pr satisfying Pr[F ≤ s] = p given r.

Mirrors CDFLIB’s cdfnbn with which = 4 (cdflib.f90:5400-5430). Caller passes both p and q = 1 − p; consistency is enforced within 3ε. When p > q the search runs on ompr = 1 − pr (F90’s variable-switch precision strategy) and returns pr = 1 − ompr.

impl NegativeBinomial

pub fn inverse_ccdf(&self, q: f64) -> Result<f64, NegativeBinomialError>

Returns the real-valued s such that cdf(s) = 1 − q on the smooth continuous extension via Iₚᵣ(r, s+1).

Mirrors CDFLIB’s cdfnbn with which = 2 (cdflib.f90:5335-5380): single dinvr loop, residual cum-p if p≤q else ccum-q.

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 Debug for NegativeBinomial

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

Formats the value using the given formatter.

impl Discrete for NegativeBinomial

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

Returns the mass Pr[X = x] at the support point x.

fn ln_pmf(&self, s: u64) -> f64

Returns the logarithm of the mass Pr[X = x]. Computing in log-space avoids underflow in the tails.

impl DiscreteCdf for NegativeBinomial

type Error = NegativeBinomialError

Domain-specific error type returned by the inverse routines.

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

Returns Pr[X ≤ x].

fn ccdf(&self, s: u64) -> f64

Returns Pr[X > x] = 1 − cdf(x).

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

Returns the smallest integer x such that cdf(x) ≥ p. At p = 0 returns 0; at p = 1 returns the supremum of support (the upper bound for distributions with finite support, u64::MAX for the unbounded ones).

impl Mean for NegativeBinomial

fn mean(&self) -> f64

Returns the expected value E[X].

impl PartialEq for NegativeBinomial

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

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Variance for NegativeBinomial

fn variance(&self) -> f64

Returns the variance Var(X) = E[(X − E[X])²].

fn std_dev(&self) -> f64

Returns the standard deviation (the square root of the variance).

impl Copy for NegativeBinomial

impl StructuralPartialEq for NegativeBinomial