@stdlib/stats-base-dists-poisson-pmf
v0.2.3TypeScript
Poisson distribution probability mass function (PMF).
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Probability Mass Function
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> [Poisson][poisson-distribution] distribution [probability mass function][pmf] (PMF).
The [probability mass function][pmf] (PMF) for a [Poisson][poisson-distribution] random variable is
where lambda > 0 is the mean parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-poisson-pmf
Usage
`javascript`
var pmf = require( '@stdlib/stats-base-dists-poisson-pmf' );
#### pmf( x, lambda )
Evaluates the [probability mass function][pmf] (PMF) of a [Poisson][poisson-distribution] distribution with mean parameter lambda.
`javascript
var y = pmf( 4.0, 3.0 );
// returns ~0.168
y = pmf( 1.0, 3.0 );
// returns ~0.149
y = pmf( -1.0, 2.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pmf( NaN, 2.0 );
// returns NaN
y = pmf( 0.0, NaN );
// returns NaN
`
If provided a negative mean parameter lambda, the function returns NaN.
`javascript
var y = pmf( 2.0, -1.0 );
// returns NaN
y = pmf( 4.0, -2.0 );
// returns NaN
`
If provided lambda = 0, the function evaluates the [PMF][pmf] of a [degenerate distribution][degenerate-distribution] centered at 0.0.
`javascript
var y = pmf( 2.0, 0.0 );
// returns 0.0
y = pmf( 0.0, 0.0 );
// returns 1.0
`
#### pmf.factory( lambda )
Returns a function for evaluating the [probability mass function][pmf] (PMF) of a [Poisson][poisson-distribution] distribution with mean parameter lambda.
`javascript
var mypmf = pmf.factory( 1.0 );
var y = mypmf( 3.0 );
// returns ~0.061
y = mypmf( 1.0 );
// returns ~0.368
`
Examples
`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-poisson-pmf' );
var opts = {
'dtype': 'float64'
};
var x = discreteUniform( 10, 0.0, 10.0, opts );
var lambda = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %d, λ: %0.4f, P(X=x;λ): %0.4f', x, lambda, pmf );
`
*
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
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-poisson-pmf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson-pmf/main/LICENSE
[degenerate-distribution]: https://en.wikipedia.org/wiki/Degenerate_distribution
[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution
[pmf]: https://en.wikipedia.org/wiki/Probability_mass_function