Struct Binomial 

pub struct Binomial { /* private fields */ }

Binomial distribution with n trials and success probability p.

Models the number of successes in a sequence of n independent Bernoulli trials. The CDF reduces to the incomplete Β (Abramowitz–Stegun 26.5.24): Pr[S ≤ s] = I₁ ₋ ₚ(n − s, s + 1).

Notes

Entropy is not implemented.

Example

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

let b = Binomial::new(10, 0.3);

// Probability of 3 or fewer successes in 10 trials
let cdf = b.cdf(3);

// Compute success probability given Pr[S ≤ 2] = 0.5 and n = 10
let pr = Binomial::search_pr(0.5, 0.5, 10, 2).unwrap();

Implementations

impl Binomial

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

Construct a Binomial(n, pr) distribution with n trials and success probability pr ∈ [0 . . 1].

Panics

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

pub fn try_new(n: u64, pr: f64) -> Result<Self, BinomialError>

Fallible counterpart of new returning a BinomialError instead of panicking.

Returns PrOutOfRange if pr falls outside [0 . . 1] or is non-finite.

pub const fn n(&self) -> u64

Returns the number of trials n.

pub const fn pr(&self) -> f64

Returns the success probability pr.

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

Returns the (continuous) number of trials n satisfying Pr[S ≤ s] = p given the success probability. The search works on the continuous extension of the CDF.

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

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

Returns the success probability pr satisfying Pr[S ≤ s] = p given n.

Mirrors CDFLIB’s cdfbin with which = 4 (cdflib.f90:3232-3265). 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 Binomial

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

Returns the real-valued s such that cdf(s) = 1 − q on the smooth continuous extension via I₁₋ₚᵣ(n−s, s+1).

Mirrors CDFLIB’s cdfbin with which = 2 (cdflib.f90:3138-3185): single dinvr loop, residual cum-p if p≤q else ccum-q.

Trait Implementations

impl Clone for Binomial

fn clone(&self) -> Binomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Binomial

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

Formats the value using the given formatter.

impl Discrete for Binomial

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 Binomial

type Error = BinomialError

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, BinomialError>

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 Binomial

fn mean(&self) -> f64

Returns the expected value E[X].

impl PartialEq for Binomial

fn eq(&self, other: &Binomial) -> 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 Binomial

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 Binomial

impl StructuralPartialEq for Binomial