npm package: @stdlib/stats-base-dists-binomial-pmf
Description: Binomial distribution probability mass function (PMF).
Author: The Stdlib Authors
Latest version: 0.3.1

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# 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] -->

> [Binomial][binomial-distribution] distribution probability mass function (PMF).

<section class="intro">

The [probability mass function][pmf] (PMF) for a [binomial][binomial-distribution] random variable is

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

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

<!-- </equation> -->

where `n` is the number of trials and `0 <= p <= 1` is the success probability.

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-base-dists-binomial-pmf
```

</section>

<section class="usage">

## Usage

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

#### pmf( x, n, p )

Evaluates the [probability mass function][pmf] (PMF) for a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.

```javascript
var y = pmf( 3.0, 20, 0.2 );
// returns ~0.205

y = pmf( 21.0, 20, 0.2 );
// returns 0.0

y = pmf( 5.0, 10, 0.4 );
// returns ~0.201

y = pmf( 0.0, 10, 0.4 );
// returns ~0.006
```

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

```javascript
var y = pmf( NaN, 20, 0.5 );
// returns NaN

y = pmf( 0.0, NaN, 0.5 );
// returns NaN

y = pmf( 0.0, 20, NaN );
// returns NaN
```

If provided a number of trials `n` which is not a nonnegative integer, the function returns `NaN`.

```javascript
var y = pmf( 2.0, 1.5, 0.5 );
// returns NaN

y = pmf( 2.0, -2.0, 0.5 );
// returns NaN
```

If provided a success probability `p` outside of `[0,1]`, the function returns `NaN`.

```javascript
var y = pmf( 2.0, 20, -1.0 );
// returns NaN

y = pmf( 2.0, 20, 1.5 );
// returns NaN
```

#### pmf.factory( n, p )

Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [binomial][binomial-distribution] distribution with number of trials `n` and success probability `p`.

```javascript
var mypmf = pmf.factory( 10, 0.5 );

var y = mypmf( 3.0 );
// returns ~0.117

y = mypmf( 5.0 );
// returns ~0.246
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pmf = require( '@stdlib/stats-base-dists-binomial-pmf' );

var opts = {
    'dtype': 'float64'
};
var x = discreteUniform( 10, 0, 20, opts );
var n = discreteUniform( 10, 0, 100, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 'x: %0.4f, n: %0.4f, p: %0.4f, P(X = x;n,p): %0.4f', x, n, p, pmf );
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/stats/base/dists/binomial/pmf.h"
```

#### stdlib_base_dists_binomial_pmf( x, n, p )

Evaluates the probability mass function (PMF) for a binomial distribution with number of trials `n` and success probability `p` at a value `x`.

```c
double out = stdlib_base_dists_binomial_pmf( 3.0, 20, 0.2 );
// returns ~0.205
```

The function accepts the following arguments:

-   **x**: `[in] double` input value.
-   **n**: `[in] int32_t` number of trials.
-   **p**: `[in] double` success probability.

```c
double stdlib_base_dists_binomial_pmf( const double x, const int32_t n, const double p );
```

</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/binomial/pmf.h"
#include <stdlib.h>
#include <stdio.h>
#include <stdint.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) );
}

static int32_t random_int( const int32_t min, const int32_t max ) {
    return min + (int32_t)( random_uniform( 0.0, 1.0 ) * ( max - min + 1 ) );
}

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

    for ( i = 0; i < 25; i++ ) {
        n = random_int( 1, 20 );
        x = random_uniform( 0.0, (double)n );
        p = random_uniform( 0.0, 1.0 );
        y = stdlib_base_dists_binomial_pmf( x, n, p );
        printf( "x: %.4f, n: %d, p: %.4f, P(X = x;n,p): %.4f\n", x, n, p, y );
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

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<section class="related">

</section>

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<section class="main-repo" >

* * *

## 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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[binomial-distribution]: https://en.wikipedia.org/wiki/Binomial_distribution

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

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