npm package: @stdlib/stats-base-dists-poisson
Description: Poisson distribution.
Author: The Stdlib Authors
Latest version: 0.3.1

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# Poisson

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> Poisson distribution.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### poisson

Poisson distribution.

```javascript
var dist = poisson;
// returns {...}
```

The namespace contains the following distribution functions:

<!-- <toc pattern="*+(cdf|pmf|mgf|quantile)*"> -->

<div class="namespace-toc">

-   <span class="signature">[`cdf( x, lambda )`][@stdlib/stats/base/dists/poisson/cdf]</span><span class="delimiter">: </span><span class="description">Poisson distribution cumulative distribution function.</span>
-   <span class="signature">[`logpmf( x, lambda )`][@stdlib/stats/base/dists/poisson/logpmf]</span><span class="delimiter">: </span><span class="description">evaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.</span>
-   <span class="signature">[`mgf( t, lambda )`][@stdlib/stats/base/dists/poisson/mgf]</span><span class="delimiter">: </span><span class="description">Poisson distribution moment-generating function (MGF).</span>
-   <span class="signature">[`pmf( x, lambda )`][@stdlib/stats/base/dists/poisson/pmf]</span><span class="delimiter">: </span><span class="description">Poisson distribution probability mass function (PMF).</span>
-   <span class="signature">[`quantile( p, lambda )`][@stdlib/stats/base/dists/poisson/quantile]</span><span class="delimiter">: </span><span class="description">Poisson distribution quantile function.</span>

</div>

<!-- </toc> -->

The namespace contains the following functions for calculating distribution properties:

<!-- <toc pattern="*+(entropy|kurtosis|mean|median|mode|skewness|stdev|variance)*"> -->

<div class="namespace-toc">

-   <span class="signature">[`entropy( lambda )`][@stdlib/stats/base/dists/poisson/entropy]</span><span class="delimiter">: </span><span class="description">Poisson distribution entropy.</span>
-   <span class="signature">[`kurtosis( lambda )`][@stdlib/stats/base/dists/poisson/kurtosis]</span><span class="delimiter">: </span><span class="description">Poisson distribution excess kurtosis.</span>
-   <span class="signature">[`mean( lambda )`][@stdlib/stats/base/dists/poisson/mean]</span><span class="delimiter">: </span><span class="description">Poisson distribution expected value.</span>
-   <span class="signature">[`median( lambda )`][@stdlib/stats/base/dists/poisson/median]</span><span class="delimiter">: </span><span class="description">Poisson distribution median.</span>
-   <span class="signature">[`mode( lambda )`][@stdlib/stats/base/dists/poisson/mode]</span><span class="delimiter">: </span><span class="description">Poisson distribution mode.</span>
-   <span class="signature">[`skewness( lambda )`][@stdlib/stats/base/dists/poisson/skewness]</span><span class="delimiter">: </span><span class="description">Poisson distribution skewness.</span>
-   <span class="signature">[`stdev( lambda )`][@stdlib/stats/base/dists/poisson/stdev]</span><span class="delimiter">: </span><span class="description">Poisson distribution standard deviation.</span>
-   <span class="signature">[`variance( lambda )`][@stdlib/stats/base/dists/poisson/variance]</span><span class="delimiter">: </span><span class="description">Poisson distribution variance.</span>

</div>

<!-- </toc> -->

The namespace contains a constructor function for creating a [Poisson][poisson-distribution] distribution object.

<!-- <toc pattern="*ctor*"> -->

<div class="namespace-toc">

-   <span class="signature">[`Poisson( [lambda] )`][@stdlib/stats/base/dists/poisson/ctor]</span><span class="delimiter">: </span><span class="description">Poisson distribution constructor.</span>

</div>

<!-- </toc> -->

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

var dist = new Poisson( 2.0 );

var y = dist.pmf( 3.0 );
// returns ~0.18

y = dist.pmf( 2.3 );
// returns 0.0
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

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

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

/*
* Let's take a customer service center example: average rate of customer inquiries is 3 per hour.
* This situation can be modeled using a Poisson distribution with λ = 3
*/

var lambda = 3;

// Mean can be used to calculate the average number of inquiries per hour:
console.log( poisson.mean( lambda ) );
// => 3

// Standard deviation can be used to calculate the measure of the spread of inquiries around the mean:
console.log( poisson.stdev( lambda ) );
// => ~1.7321

// Variance can be used to calculate the variability of the number of inquiries:
console.log( poisson.variance( lambda ) );
// => 3

// PMF can be used to calculate specific number of inquiries in an hour:
console.log( poisson.pmf( 4, lambda ) );
// => ~0.1680

// CDF can be used to calculate probability up to certain number of inquiries in an hour:
console.log( poisson.cdf( 2, lambda ) );
// => ~0.4232

// Quantile can be used to calculate the number of inquiries at which you can be 80% confident that the actual number will not exceed.
console.log( poisson.quantile( 0.8, lambda ) );
// => 4

// MGF can be used for more advanced statistical analyses and generating moments of the distribution.
console.log( poisson.mgf( 1.0, lambda ) );
// => ~173.2690
```

</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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* * *

## Notice

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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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[poisson-distribution]: https://en.wikipedia.org/wiki/Poisson_distribution

<!-- <toc-links> -->

[@stdlib/stats/base/dists/poisson/ctor]: https://www.npmjs.com/package/@stdlib/stats-base-dists-poisson-ctor

[@stdlib/stats/base/dists/poisson/entropy]: https://www.npmjs.com/package/@stdlib/stats-base-dists-poisson-entropy

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[@stdlib/stats/base/dists/poisson/mode]: https://www.npmjs.com/package/@stdlib/stats-base-dists-poisson-mode

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[@stdlib/stats/base/dists/poisson/logpmf]: https://www.npmjs.com/package/@stdlib/stats-base-dists-poisson-logpmf

[@stdlib/stats/base/dists/poisson/mgf]: https://www.npmjs.com/package/@stdlib/stats-base-dists-poisson-mgf

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