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# 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 ) );
}
```

## 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.

#### Community

## License

See LICENSE.

## Copyright

Copyright © 2016-2024. The Stdlib Authors.