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

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# Geometric

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

> Geometric 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>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### Geometric( \[p] )

Returns a [geometric][geometric-distribution] distribution object.

```javascript
var geometric = new Geometric();

var mean = geometric.mean;
// returns 1.0
```

By default, `p = 0.5`. To create a distribution having a different success probability `p`, provide a parameter value.

```javascript
var geometric = new Geometric( 0.2 );

var mean = geometric.mean;
// returns 4.0
```

* * *

## geometric

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

### Writable Properties

#### geometric.p

Success probability of the distribution. `p` **must** be a probability.

```javascript
var geometric = new Geometric( 0.2 );

var p = geometric.p;
// returns 0.2

geometric.p = 0.3;

p = geometric.p;
// returns 0.3
```

* * *

### Computed Properties

#### Geometric.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var geometric = new Geometric( 0.4 );

var entropy = geometric.entropy;
// returns ~1.683
```

#### Geometric.prototype.kurtosis

Returns the [excess kurtosis][kurtosis].

```javascript
var geometric = new Geometric( 0.4 );

var kurtosis = geometric.kurtosis;
// returns ~6.267
```

#### Geometric.prototype.mean

Returns the [median][expected-value].

```javascript
var geometric = new Geometric( 0.4 );

var mu = geometric.mean;
// returns ~1.5
```

#### Geometric.prototype.median

Returns the [median][median].

```javascript
var geometric = new Geometric( 0.4 );

var median = geometric.median;
// returns 1.0
```

#### Geometric.prototype.mode

Returns the [mode][mode].

```javascript
var geometric = new Geometric( 0.4 );

var mode = geometric.mode;
// returns 0.0
```

#### Geometric.prototype.skewness

Returns the [skewness][skewness].

```javascript
var geometric = new Geometric( 0.4 );

var skewness = geometric.skewness;
// returns ~2.066
```

#### Geometric.prototype.stdev

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

```javascript
var geometric = new Geometric( 0.4 );

var s = geometric.stdev;
// returns ~1.936
```

#### Geometric.prototype.variance

Returns the [variance][variance].

```javascript
var geometric = new Geometric( 0.4 );

var s2 = geometric.variance;
// returns ~3.75
```

* * *

### Methods

#### Geometric.prototype.cdf( x )

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

```javascript
var geometric = new Geometric( 0.2 );

var y = geometric.cdf( 0.5 );
// returns ~0.2
```

#### Geometric.prototype.logcdf( x )

Evaluates the natural logarithm of the [cumulative distribution function][cdf] (logCDF).

```javascript
var geometric = new Geometric( 0.2 );

var y = geometric.logcdf( 0.5 );
// returns ~-1.609
```

#### Geometric.prototype.logpmf( x )

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

```javascript
var geometric = new Geometric( 0.2 );

var y = geometric.logpmf( 3.0 );
// returns ~-2.279

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

#### Geometric.prototype.mgf( t )

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

```javascript
var geometric = new Geometric( 0.2 );

var y = geometric.mgf( 0.1 );
// returns ~1.908
```

#### Geometric.prototype.pmf( x )

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

```javascript
var geometric = new Geometric( 0.2 );

var y = geometric.pmf( 3.0 );
// returns ~0.102

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

#### Geometric.prototype.quantile( p )

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

```javascript
var geometric = new Geometric( 0.2 );

var y = geometric.quantile( 0.5 );
// returns 3.0

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

</section>

<!-- /.usage -->

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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 Geometric = require( '@stdlib/stats-base-dists-geometric-ctor' );

var geometric = new Geometric( 0.5 );

var mu = geometric.mean;
// returns 1.0

var mode = geometric.mode;
// returns 0.0

var s2 = geometric.variance;
// returns 2.0

var y = geometric.cdf( 2.0 );
// returns 0.875
```

</section>

<!-- /.examples -->

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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-geometric-ctor/main/LICENSE

[geometric-distribution]: https://en.wikipedia.org/wiki/Geometric_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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