npm package: @stdlib/stats-base-dists-poisson-ctor
Description: Poisson distribution constructor.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Poisson

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Poisson distribution constructor.

<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->

<section class="intro">

</section>

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<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### Poisson( \[lambda] )

Returns an [Poisson][poisson-distribution] distribution object.

```javascript
var poisson = new Poisson();

var lambda = poisson.mean;
// returns 1.0
```

By default, `lambda = 1.0`. To create a distribution having a different mean parameter `lambda`, provide a parameter value.

```javascript
var poisson = new Poisson( 4.0 );

var lambda = poisson.mean;
// returns 4.0
```

* * *

## poisson

A [Poisson][poisson-distribution] distribution object has the following properties and methods...

### Writable Properties

#### poisson.lambda

Mean parameter of the distribution. `lambda` **must** be a positive number.

```javascript
var poisson = new Poisson( 2.0 );

var lambda = poisson.lambda;
// returns 2.0

poisson.lambda = 3.0;

lambda = poisson.lambda;
// returns 3.0
```

* * *

### Computed Properties

#### Poisson.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var poisson = new Poisson( 4.0 );

var entropy = poisson.entropy;
// returns ~2.087
```

#### Poisson.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var poisson = new Poisson( 4.0 );

var kurtosis = poisson.kurtosis;
// returns 0.25
```

#### Poisson.prototype.mean

Returns the [median][expected-value].

```javascript
var poisson = new Poisson( 4.0 );

var mu = poisson.mean;
// returns 4.0
```

#### Poisson.prototype.median

Returns the [median][median].

```javascript
var poisson = new Poisson( 4.0 );

var median = poisson.median;
// returns 4.0
```

#### Poisson.prototype.mode

Returns the [mode][mode].

```javascript
var poisson = new Poisson( 4.0 );

var mode = poisson.mode;
// returns 4.0
```

#### Poisson.prototype.skewness

Returns the [skewness][skewness].

```javascript
var poisson = new Poisson( 4.0 );

var skewness = poisson.skewness;
// returns 0.5
```

#### Poisson.prototype.stdev

Returns the [standard deviation][standard-deviation].

```javascript
var poisson = new Poisson( 4.0 );

var s = poisson.stdev;
// returns 2.0
```

#### Poisson.prototype.variance

Returns the [variance][variance].

```javascript
var poisson = new Poisson( 4.0 );

var s2 = poisson.variance;
// returns 4.0
```

* * *

### Methods

#### Poisson.prototype.cdf( x )

Evaluates the [cumulative distribution function][cdf] (CDF).

```javascript
var poisson = new Poisson( 2.0 );

var y = poisson.cdf( 0.5 );
// returns ~0.135
```

#### Poisson.prototype.logpmf( x )

Evaluates the natural logarithm of the [probability mass function][pmf] (PMF).

```javascript
var poisson = new Poisson( 2.0 );

var y = poisson.logpmf( 3.0 );
// returns ~-1.712

y = poisson.logpmf( 2.3 );
// returns -Infinity
```

#### Poisson.prototype.mgf( t )

Evaluates the [moment-generating function][mgf] (MGF).

```javascript
var poisson = new Poisson( 2.0 );

var y = poisson.mgf( 0.5 );
// returns ~3.66
```

#### Poisson.prototype.pmf( x )

Evaluates the [probability mass function][pmf] (PMF).

```javascript
var poisson = new Poisson( 2.0 );

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

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

#### Poisson.prototype.quantile( p )

Evaluates the [quantile function][quantile-function] at probability `p`.

```javascript
var poisson = new Poisson( 2.0 );

var y = poisson.quantile( 0.5 );
// returns 2.0

y = poisson.quantile( 1.9 );
// returns NaN
```

</section>

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<section class="notes">

</section>

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<!-- Package usage examples. -->

* * *

<section class="examples">

## Examples

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

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

var poisson = new Poisson( 2.0 );

var mu = poisson.mean;
// returns 2.0

var mode = poisson.mode;
// returns 2.0

var s2 = poisson.variance;
// returns 2.0

var y = poisson.cdf( 0.8 );
// returns ~0.135
```

</section>

<!-- /.examples -->

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</section>

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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

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-poisson-ctor/main/LICENSE

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

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function

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

[quantile-function]: https://en.wikipedia.org/wiki/Quantile_function

[entropy]: https://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[expected-value]: https://en.wikipedia.org/wiki/Expected_value

[kurtosis]: https://en.wikipedia.org/wiki/Kurtosis

[median]: https://en.wikipedia.org/wiki/Median

[mode]: https://en.wikipedia.org/wiki/Mode_%28statistics%29

[skewness]: https://en.wikipedia.org/wiki/Skewness

[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation

[variance]: https://en.wikipedia.org/wiki/Variance

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