npm package: @stdlib/stats-base-dists-hypergeometric-logpmf
Description: Natural logarithm of the probability mass function (PMF) for a hypergeometric distribution.
Author: The Stdlib Authors
Latest version: 0.1.3

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# Logarithm of Probability Mass Function

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Evaluate the natural logarithm of the [probability mass function][pmf] (PMF) for a [hypergeometric][hypergeometric-distribution] distribution.

<section class="intro">

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

<!-- <equation class="equation" label="eq:hypergeometric_pmf" align="center" raw="f(x;N,K,n)=P(X=x;N,K,n)=\begin{cases} {{{K \choose x} {N-K \choose {n-x}}}\over {{N} \choose n}} & \text{ for } x = 0,1,2,\ldots \\ 0 & \text{ otherwise} \end{cases}" alt="Probability mass function (PMF) for a hypergeometric distribution."> -->

<div class="equation" align="center" data-raw-text="f(x;N,K,n)=P(X=x;N,K,n)=\begin{cases} {{{K \choose x} {N-K \choose {n-x}}}\over {{N} \choose n}} &amp; \text{ for } x = 0,1,2,\ldots \\ 0 &amp; \text{ otherwise} \end{cases}" data-equation="eq:hypergeometric_pmf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/hypergeometric/logpmf/docs/img/equation_hypergeometric_pmf.svg" alt="Probability mass function (PMF) for a hypergeometric distribution.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-hypergeometric-logpmf
```

</section>

<section class="usage">

## Usage

```javascript
var logpmf = require( '@stdlib/stats-base-dists-hypergeometric-logpmf' );
```

#### logpmf( x, N, K, n )

Evaluates the natural logarithm of 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 = logpmf( 1.0, 8, 4, 2 );
// returns ~-0.56

y = logpmf( 2.0, 8, 4, 2 );
// returns ~-1.54

y = logpmf( 0.0, 8, 4, 2 );
// returns ~-1.54

y = logpmf( 1.5, 8, 4, 2 );
// returns -Infinity
```

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

```javascript
var y = logpmf( NaN, 10, 5, 2 );
// returns NaN

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

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

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

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

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

If the number of draws `n` or the subpopulation size `K` exceed population size `N`, the function returns `NaN`.

```javascript
var y = logpmf( 2.0, 10, 5, 12 );
// returns NaN

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

#### logpmf.factory( N, K, n )

Returns a function for evaluating the natural logarithm of 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 mylogpmf = logpmf.factory( 30, 20, 5 );
var y = mylogpmf( 4.0 );
// returns ~-1.079

y = mylogpmf( 1.0 );
// returns ~-3.524
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

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

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 = logpmf( x, N, K, n );
    console.log( 'x: %d, N: %d, K: %d, n: %d, ln(P(X=x;N,K,n)): %d', x, N, K, n, y.toFixed( 4 ) );
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

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<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/hypergeometric/logpmf.h"
```

#### stdlib_base_dists_hypergeometric_logpmf( x, N, K, n )

Evaluates the natural logarithm of 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_logpmf( 1.0, 8, 4, 2 );
// returns ~-0.56
```

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.

```c
double stdlib_base_dists_hypergeometric_logpmf( const double x, const int32_t N, const int32_t K, const int32_t n );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/stats/base/dists/hypergeometric/logpmf.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 y;
    double x;
    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_logpmf( x, N, K, n );
        printf( "x: %lf, N: %d, K: %d, n: %d, ln(P(X=x;N,K,n)): %lf\n", x, N, K, n, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

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* * *

## 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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-hypergeometric-logpmf/main/LICENSE

[hypergeometric-distribution]: https://en.wikipedia.org/wiki/Hypergeometric_distribution

[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function

</section>

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