Probability Mass Function

Hypergeometric distribution probability mass function (PMF).

Imagine a scenario with a population of size N, of which a subpopulation of size K can be considered successes. We draw n observations from the total population. Defining the random variable X as the number of successes in the n draws, X is said to follow a hypergeometric distribution. The probability mass function (PMF) for a hypergeometric random variable is given by

Installation

npm install @stdlib/stats-base-dists-hypergeometric-pmf

Usage

var pmf = require( '@stdlib/stats-base-dists-hypergeometric-pmf' );

pmf( x, N, K, n )

Evaluates the probability mass function (PMF) for a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

var y = pmf( 1.0, 8, 4, 2 );
// returns ~0.571

y = pmf( 2.0, 8, 4, 2 );
// returns ~0.214

y = pmf( 0.0, 8, 4, 2 );
// returns ~0.214

y = pmf( 1.5, 8, 4, 2 );
// returns 0.0

If provided NaN as any argument, the function returns NaN.

var y = pmf( NaN, 10, 5, 2 );
// returns NaN

y = pmf( 0.0, NaN, 5, 2 );
// returns NaN

y = pmf( 0.0, 10, NaN, 2 );
// returns NaN

y = pmf( 0.0, 10, 5, NaN );
// returns NaN

If provided a population size N, subpopulation size K or draws n which is not a nonnegative integer, the function returns NaN.

var y = pmf( 2.0, 10.5, 5, 2 );
// returns NaN

y = pmf( 2.0, 10, 1.5, 2 );
// returns NaN

y = pmf( 2.0, 10, 5, -2.0 );
// returns NaN

If the number of draws n exceeds population size N, the function returns NaN.

var y = pmf( 2.0, 10, 5, 12 );
// returns NaN

y = pmf( 2.0, 8, 3, 9 );
// returns NaN

pmf.factory( N, K, n )

Returns a function for evaluating the probability mass function (PMF) of a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

var mypmf = pmf.factory( 30, 20, 5 );
var y = mypmf( 4.0 );
// returns ~0.34

y = mypmf( 1.0 );
// returns ~0.029

Examples

var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var pmf = require( '@stdlib/stats-base-dists-hypergeometric-pmf' );

var i;
var N;
var K;
var n;
var x;
var y;

for ( i = 0; i < 10; i++ ) {
    x = round( randu() * 5.0 );
    N = round( randu() * 20.0 );
    K = round( randu() * N );
    n = round( randu() * N );
    y = pmf( x, N, K, n );
    console.log( 'x: %d, N: %d, K: %d, n: %d, P(X=x;N,K,n): %d', x, N, K, n, y.toFixed( 4 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/hypergeometric/pmf.h"

stdlib_base_dists_hypergeometric_pmf( x, N, K, n )

Evaluates the probability mass function (PMF) for a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

double out = stdlib_base_dists_hypergeometric_pmf( 1.0, 8, 4, 2 );
// returns ~0.571

The function accepts the following arguments:

• x: [in] double input value.
• N: [in] int32_t population size.
• K: [in] int32_t subpopulation size.
• n: [in] int32_t number of draws.

double stdlib_base_dists_hypergeometric_pmf( const double x, const int32_t N, const int32_t K, const int32_t n );

Examples

#include "stdlib/stats/base/dists/hypergeometric/pmf.h"
#include "stdlib/math/base/special/round.h"
#include <stdlib.h>
#include <stdint.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v * ( max - min ) );
}

int main( void ) {
    int32_t N;
    int32_t K;
    int32_t n;
    double x;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        x = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
        N = stdlib_base_round( random_uniform( 0.0, 20.0 ) );
        K = stdlib_base_round( random_uniform( 0.0, N ) );
        n = stdlib_base_round( random_uniform( 0.0, N ) );
        y = stdlib_base_dists_hypergeometric_pmf( x, N, K, n );
        printf( "x: %lf, N: %d, K: %d, n: %d, P(X=x;N,K,n): %lf\n", x, N, K, n, y );
    }
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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License

See LICENSE.

Copyright

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