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

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# Cauchy

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> Cauchy distribution.

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### cauchy

Cauchy distribution.

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

The namespace contains the following distribution functions:

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

<div class="namespace-toc">

-   <span class="signature">[`cdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/cdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution cumulative distribution function.</span>
-   <span class="signature">[`logcdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/logcdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution logarithm of cumulative distribution function.</span>
-   <span class="signature">[`logpdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/logpdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution logarithm of probability density function (logPDF).</span>
-   <span class="signature">[`pdf( x, x0, gamma )`][@stdlib/stats/base/dists/cauchy/pdf]</span><span class="delimiter">: </span><span class="description">Cauchy distribution probability density function (PDF).</span>
-   <span class="signature">[`quantile( p, x0, gamma )`][@stdlib/stats/base/dists/cauchy/quantile]</span><span class="delimiter">: </span><span class="description">Cauchy 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( x0, gamma )`][@stdlib/stats/base/dists/cauchy/entropy]</span><span class="delimiter">: </span><span class="description">Cauchy distribution differential entropy.</span>
-   <span class="signature">[`median( x0, gamma )`][@stdlib/stats/base/dists/cauchy/median]</span><span class="delimiter">: </span><span class="description">Cauchy distribution median.</span>
-   <span class="signature">[`mode( x0, gamma )`][@stdlib/stats/base/dists/cauchy/mode]</span><span class="delimiter">: </span><span class="description">Cauchy distribution mode.</span>

</div>

<!-- </toc> -->

The namespace contains a constructor function for creating a [Cauchy][cauchy-distribution] distribution object.

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

<div class="namespace-toc">

-   <span class="signature">[`Cauchy( [x0, gamma] )`][@stdlib/stats/base/dists/cauchy/ctor]</span><span class="delimiter">: </span><span class="description">Cauchy distribution constructor.</span>

</div>

<!-- </toc> -->

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

var dist = new Cauchy( 2.0, 4.0 );

var median = dist.median;
// returns 2.0
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- TODO: better examples -->

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

```javascript
var objectKeys = require( '@stdlib/utils-keys' );
var cauchy = require( '@stdlib/stats-base-dists-cauchy' );

console.log( objectKeys( cauchy ) );
```

</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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<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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

</section>

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[cauchy-distribution]: https://en.wikipedia.org/wiki/Cauchy_distribution

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

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

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

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

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

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</section>

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