npm package: @stdlib/stats-base-dists-binomial-logpmf
Description: Natural logarithm of the probability mass function (PMF) for a binomial distribution.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Logarithm of Probability Mass Function

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

<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/logpmf/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-logpmf
```

</section>

<section class="usage">

## Usage

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

#### logpmf( x, n, p )

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

```javascript
var y = logpmf( 3.0, 20, 0.2 );
// returns ~-1.583

y = logpmf( 21.0, 20, 0.2 );
// returns -Infinity

y = logpmf( 5.0, 10, 0.4 );
// returns ~-1.606

y = logpmf( 0.0, 10, 0.4 );
// returns ~-5.108
```

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

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

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

y = logpmf( 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 = logpmf( 2.0, 1.5, 0.5 );
// returns NaN

y = logpmf( 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 = logpmf( 2.0, 20, -1.0 );
// returns NaN

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

#### logpmf.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 mylogpmf = logpmf.factory( 10, 0.5 );

var y = mylogpmf( 3.0 );
// returns ~-2.144

y = mylogpmf( 5.0 );
// returns ~-1.402
```

</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 logpmf = require( '@stdlib/stats-base-dists-binomial-logpmf' );

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

</section>

<!-- /.examples -->

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

<section class="related">

</section>

<!-- /.related -->

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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].

#### Community

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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-binomial-logpmf/main/LICENSE

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

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

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