@stdlib/stats-base-dists-hypergeometric-pmf
v0.3.1TypeScript
Hypergeometric distribution probability mass function (PMF).
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Published by The Stdlib Authors
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Probability Mass Function
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> [Hypergeometric][hypergeometric-distribution] distribution [probability mass function][pmf] (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][hypergeometric-distribution]. The [probability mass function][pmf] (PMF) for a [hypergeometric][hypergeometric-distribution] random variable is given by
Installation
``bash`
npm install @stdlib/stats-base-dists-hypergeometric-pmf
Usage
`javascript`
var pmf = require( '@stdlib/stats-base-dists-hypergeometric-pmf' );
#### pmf( x, N, K, n )
Evaluates the [probability mass function][pmf] (PMF) for a [hypergeometric][hypergeometric-distribution] distribution with parameters N (population size), K (subpopulation size), and n (number of draws).
`javascript
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.
`javascript
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.
`javascript
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.
`javascript
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] (PMF) of a [hypergeometric ][hypergeometric-distribution] distribution with parameters N (population size), K (subpopulation size), and n (number of draws).
`javascript
var mypmf = pmf.factory( 30, 20, 5 );
var y = mypmf( 4.0 );
// returns ~0.34
y = mypmf( 1.0 );
// returns ~0.029
`
Examples
`javascript
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
$3
`c`
#include "stdlib/stats/base/dists/hypergeometric/pmf.h"
#### stdlib_base_dists_hypergeometric_pmf( x, N, K, n )
Evaluates the [probability mass function][pmf] (PMF) for a [hypergeometric][hypergeometric-distribution] distribution with parameters N (population size), K (subpopulation size), and n (number of draws).
`c`
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.[in] int32_t
- N: population size.[in] int32_t
- K: subpopulation size.[in] int32_t
- n: number of draws.
`c`
double stdlib_base_dists_hypergeometric_pmf( const double x, const int32_t N, const int32_t K, const int32_t n );
$3
`c
#include "stdlib/stats/base/dists/hypergeometric/pmf.h"
#include "stdlib/math/base/special/round.h"
#include
#include
#include
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][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][stdlib], see the main project [repository][stdlib].
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---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[hypergeometric-distribution]: https://en.wikipedia.org/wiki/Hypergeometric_distribution
[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function