# @stdlib/stats-base-dists-poisson-logpmf

0.2.1 • Public • Published
About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

# Logarithm of Probability Mass Function

Evaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.

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

where `lambda > 0` is the mean parameter.

## Installation

`npm install @stdlib/stats-base-dists-poisson-logpmf`

## Usage

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

#### logpmf( x, lambda )

Evaluates the natural logarithm of the probability mass function (PMF) for a Poisson distribution with mean parameter `lambda`.

```var y = logpmf( 4.0, 3.0 );
// returns ~-1.784

y = logpmf( 1.0, 3.0 );
// returns ~-1.901

y = logpmf( -1.0, 2.0 );
// returns -Infinity```

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

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

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

If provided a negative mean parameter `lambda`, the function returns `NaN`.

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

y = logpmf( 4.0, -2.0 );
// returns NaN```

If provided `lambda = 0`, the function evaluates the natural logarithm of the PMF of a degenerate distribution centered at `0.0`.

```var y = logpmf( 2.0, 0.0 );
// returns -Infinity

y = logpmf( 0.0, 0.0 );
// returns 0.0```

#### logpmf.factory( lambda )

Returns a function for evaluating the natural logarithm of the probability mass function (PMF) for a Poisson distribution with mean parameter `lambda`.

```var mylogpmf = logpmf.factory( 1.0 );
var y = mylogpmf( 3.0 );
// returns ~-2.792

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

## Examples

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

var lambda;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = round( randu() * 10.0 );
lambda = randu() * 10.0;
y = logpmf( x, lambda );
console.log( 'x: %d, λ: %d, ln(P(X=x;λ)): %d', x, lambda.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 © 2016-2024. The Stdlib Authors.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-poisson-logpmf`

stdlib.io

74

0.2.1

Apache-2.0

55.7 kB

13