@stdlib/stats/base/dists/poisson/README.md

Standard library statistical functions.

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# Poisson

> Poisson distribution.

<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>

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The namespace contains the following functions for calculating distribution properties:

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<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>

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

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<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 -->

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<section class="related">

</section>

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<section class="links">

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

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

[@stdlib/stats/base/dists/poisson/ctor]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/ctor

[@stdlib/stats/base/dists/poisson/entropy]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/entropy

[@stdlib/stats/base/dists/poisson/kurtosis]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/kurtosis

[@stdlib/stats/base/dists/poisson/mean]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/mean

[@stdlib/stats/base/dists/poisson/median]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/median

[@stdlib/stats/base/dists/poisson/mode]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/mode

[@stdlib/stats/base/dists/poisson/skewness]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/skewness

[@stdlib/stats/base/dists/poisson/stdev]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/stdev

[@stdlib/stats/base/dists/poisson/variance]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/variance

[@stdlib/stats/base/dists/poisson/cdf]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/cdf

[@stdlib/stats/base/dists/poisson/logpmf]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/logpmf

[@stdlib/stats/base/dists/poisson/mgf]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/mgf

[@stdlib/stats/base/dists/poisson/pmf]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/pmf

[@stdlib/stats/base/dists/poisson/quantile]: https://github.com/stdlib-js/stats/tree/main/base/dists/poisson/quantile

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</section>

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