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# npm

## @stdlib/stats-base-dists-binomial-pmf

0.0.6 • Public • Published

# Probability Mass Function

Binomial distribution probability mass function (PMF).

The probability mass function (PMF) for a binomial random variable is

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

## Installation

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

## Usage

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

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

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

```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`.

```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`.

```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`.

```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) of a binomial distribution with number of trials `n` and success probability `p`.

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

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

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

## Examples

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

var i;
var n;
var p;
var x;
var y;

for ( i = 0; i < 10; i++ ) {
x = round( randu() * 20.0 );
n = round( randu() * 100.0 );
p = randu();
y = pmf( x, n, p );
console.log( 'x: %d, n: %d, p: %d, P(X = x;n,p): %d', x, n, p.toFixed( 4 ), 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.

See LICENSE.

## Copyright

Copyright © 2016-2022. The Stdlib Authors.

### Install

`npm i @stdlib/stats-base-dists-binomial-pmf`

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