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

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# Cauchy

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> Cauchy distribution constructor.

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<section class="intro">

</section>

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<!-- Package usage documentation. -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

#### Cauchy( \[x0, gamma] )

Returns a [Cauchy][cauchy-distribution] distribution object.

```javascript
var cauchy = new Cauchy();

var median = cauchy.median;
// returns 0.0
```

By default, `x0 = 0.0` and `gamma = 1.0`. To create a distribution having a different `x0` (location parameter) and `gamma` (scale parameter), provide the corresponding arguments.

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

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

* * *

## cauchy

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

### Writable Properties

#### cauchy.x0

Location parameter of the distribution.

```javascript
var cauchy = new Cauchy();

var x0 = cauchy.x0;
// returns 0.0

cauchy.x0 = 3.0;

x0 = cauchy.x0;
// returns 3.0
```

#### cauchy.gamma

Scale parameter of the distribution. `gamma` **must** be a positive number.

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

var gamma = cauchy.gamma;
// returns 4.0

cauchy.gamma = 3.0;

gamma = cauchy.gamma;
// returns 3.0
```

* * *

### Computed Properties

#### Cauchy.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var cauchy = new Cauchy( 4.0, 12.0 );

var entropy = cauchy.entropy;
// returns ~5.016
```

#### Cauchy.prototype.median

Returns the [median][median].

```javascript
var cauchy = new Cauchy( 4.0, 12.0 );

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

#### Cauchy.prototype.mode

Returns the [mode][mode].

```javascript
var cauchy = new Cauchy( 4.0, 12.0 );

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

* * *

### Methods

#### Cauchy.prototype.cdf( x )

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

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.cdf( 0.5 );
// returns ~0.386
```

#### Cauchy.prototype.logcdf( x )

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

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.logcdf( 0.5 );
// returns ~-0.952
```

#### Cauchy.prototype.logpdf( x )

Evaluates the natural logarithm of the [probability density function][pdf] (PDF).

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.logpdf( 0.8 );
// returns ~-2.617
```

#### Cauchy.prototype.pdf( x )

Evaluates the [probability density function][pdf] (PDF).

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

var y = cauchy.pdf( 0.8 );
// returns ~0.073
```

#### Cauchy.prototype.quantile( p )

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

```javascript
var cauchy = new Cauchy( 2.0, 4.0 );

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

y = cauchy.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 Cauchy = require( '@stdlib/stats-base-dists-cauchy-ctor' );

var cauchy = new Cauchy( 2.0, 4.0 );

var entropy = cauchy.entropy;
// returns ~3.917

var median = cauchy.median;
// returns 2.0

var mode = cauchy.mode;
// returns 2.0

var y = cauchy.cdf( 0.8 );
// returns ~0.407
```

</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].

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

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

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

[pdf]: https://en.wikipedia.org/wiki/Probability_density_function

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

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

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

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

</section>

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