Struct Hypergeometric 

pub struct Hypergeometric { /* private fields */ }

Implements the Hypergeometric distribution

Examples

use statrs::distribution::{Hypergeometric, Discrete};
use statrs::statistics::Distribution;
use statrs::prec;

let n = Hypergeometric::new(500, 50, 100).unwrap();
assert_eq!(n.mean().unwrap(), 10.);
assert!(prec::almost_eq(n.pmf(10), 0.14736784, 1e-8));
assert!(prec::almost_eq(n.pmf(25), 3.537e-7, 1e-10));

Implementations

impl Hypergeometric

pub fn new( population: u64, successes: u64, draws: u64, ) -> Result<Hypergeometric, HypergeometricError>

Constructs a new hypergeometric distribution with a population (N) of population, number of successes (K) of successes, and number of draws (n) of draws.

Errors

If successes > population or draws > population.

Examples

use statrs::distribution::Hypergeometric;

let mut result = Hypergeometric::new(2, 2, 2);
assert!(result.is_ok());

result = Hypergeometric::new(2, 3, 2);
assert!(result.is_err());

pub fn population(&self) -> u64

Returns the population size of the hypergeometric distribution

Examples

use statrs::distribution::Hypergeometric;

let n = Hypergeometric::new(10, 5, 3).unwrap();
assert_eq!(n.population(), 10);

pub fn successes(&self) -> u64

Returns the number of observed successes of the hypergeometric distribution

Examples

use statrs::distribution::Hypergeometric;

let n = Hypergeometric::new(10, 5, 3).unwrap();
assert_eq!(n.successes(), 5);

pub fn draws(&self) -> u64

Returns the number of draws of the hypergeometric distribution

Examples

use statrs::distribution::Hypergeometric;

let n = Hypergeometric::new(10, 5, 3).unwrap();
assert_eq!(n.draws(), 3);

Trait Implementations

impl Clone for Hypergeometric

fn clone(&self) -> Hypergeometric

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Hypergeometric

impl Debug for Hypergeometric

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

Formats the value using the given formatter.

impl Discrete<u64, f64> for Hypergeometric

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

Calculates the probability mass function for the hypergeometric distribution at x

Formula

(K choose x) * (N-K choose n-x) / (N choose n)

where N is population, K is successes, and n is draws

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

Calculates the log probability mass function for the hypergeometric distribution at x

Formula

ln((K choose x) * (N-K choose n-x) / (N choose n))

where N is population, K is successes, and n is draws

impl DiscreteCDF<u64, f64> for Hypergeometric

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

Calculates the cumulative distribution function for the hypergeometric distribution at x

Formula

1 - ((n choose x+1) * (N-n choose K-x-1)) / (N choose K) * 3_F_2(1,
x+1-K, x+1-n; k+2, N+x+2-K-n; 1)

where N is population, K is successes, n is draws, and p_F_q is the generalized hypergeometric function

Calculated as a discrete integral over the probability mass function evaluated from 0..x+1

fn sf(&self, x: u64) -> f64

Calculates the survival function for the hypergeometric distribution at x

Formula

1 - ((n choose x+1) * (N-n choose K-x-1)) / (N choose K) * 3_F_2(1,
x+1-K, x+1-n; x+2, N+x+2-K-n; 1)

where N is population, K is successes, n is draws, and p_F_q is the generalized hypergeometric function

Calculated as a discrete integral over the probability mass function evaluated from (x+1)..max

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved Specialized inverse cdfs should be used whenever possible.

impl Display for Hypergeometric

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

Formats the value using the given formatter.

impl Distribution<f64> for Hypergeometric

Available on crate feature rand only.

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Distribution<f64> for Hypergeometric

fn mean(&self) -> Option<f64>

Returns the mean of the hypergeometric distribution

None

If N is 0

Formula

K * n / N

where N is population, K is successes, and n is draws

fn variance(&self) -> Option<f64>

Returns the variance of the hypergeometric distribution

None

If N <= 1

Formula

n * (K / N) * ((N - K) / N) * ((N - n) / (N - 1))

where N is population, K is successes, and n is draws

fn skewness(&self) -> Option<f64>

Returns the skewness of the hypergeometric distribution

None

If N <= 2

Formula

((N - 2K) * (N - 1)^(1 / 2) * (N - 2n)) / ([n * K * (N - K) * (N -
n)]^(1 / 2) * (N - 2))

where N is population, K is successes, and n is draws

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

fn entropy(&self) -> Option<T>

Returns the entropy, if it exists.

impl Distribution<u64> for Hypergeometric

Available on crate feature rand only.

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Eq for Hypergeometric

impl Max<u64> for Hypergeometric

fn max(&self) -> u64

Returns the maximum value in the domain of the hypergeometric distribution representable by a 64-bit integer

Formula

min(K, n)

where K is successes and n is draws

impl Min<u64> for Hypergeometric

fn min(&self) -> u64

Returns the minimum value in the domain of the hypergeometric distribution representable by a 64-bit integer

Formula

max(0, n + K - N)

where N is population, K is successes, and n is draws

impl Mode<Option<u64>> for Hypergeometric

fn mode(&self) -> Option<u64>

Returns the mode of the hypergeometric distribution

Formula

floor((n + 1) * (k + 1) / (N + 2))

where N is population, K is successes, and n is draws

impl PartialEq for Hypergeometric

fn eq(&self, other: &Hypergeometric) -> 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 StructuralPartialEq for Hypergeometric