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

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# Lévy

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

> Lévy 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-levy-ctor
```

</section>

<section class="usage">

## Usage

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

#### Levy( \[mu, c] )

Returns a [Lévy][levy-distribution] distribution object.

```javascript
var levy = new Levy();

var median = levy.median;
// returns ~2.198
```

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var median = levy.median;
// returns ~10.792
```

* * *

## levy

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

### Writable Properties

#### levy.mu

Location parameter of the distribution.

```javascript
var levy = new Levy();

var mu = levy.mu;
// returns 0.0

levy.mu = 3.0;

mu = levy.mu;
// returns 3.0
```

#### levy.c

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var c = levy.c;
// returns 4.0

levy.c = 3.0;

c = levy.c;
// returns 3.0
```

* * *

### Computed Properties

#### Levy.prototype.entropy

Returns the [differential entropy][entropy].

```javascript
var levy = new Levy( 4.0, 12.0 );

var entropy = levy.entropy;
// returns ~5.809
```

#### Levy.prototype.mean

Returns the [expected value][expected-value].

```javascript
var levy = new Levy( 4.0, 12.0 );

var mu = levy.mean;
// returns Infinity
```

#### Levy.prototype.median

Returns the [median][median].

```javascript
var levy = new Levy( 4.0, 12.0 );

var median = levy.median;
// returns ~30.377
```

#### Levy.prototype.mode

Returns the [mode][mode].

```javascript
var levy = new Levy( 4.0, 12.0 );

var mode = levy.mode;
// returns 8.0
```

#### Levy.prototype.stdev

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

```javascript
var levy = new Levy( 4.0, 12.0 );

var s = levy.stdev;
// returns Infinity
```

#### Levy.prototype.variance

Returns the [variance][variance].

```javascript
var levy = new Levy( 4.0, 12.0 );

var s2 = levy.variance;
// returns Infinity
```

* * *

### Methods

#### Levy.prototype.cdf( x )

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var y = levy.cdf( 2.5 );
// returns ~0.005
```

#### Levy.prototype.logcdf( x )

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var y = levy.logcdf( 2.5 );
// returns ~-5.365
```

#### Levy.prototype.logpdf( x )

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var y = levy.logpdf( 2.2 );
// returns ~-7.812
```

#### Levy.prototype.pdf( x )

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var y = levy.pdf( 2.5 );
// returns ~0.041
```

#### Levy.prototype.quantile( p )

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

```javascript
var levy = new Levy( 2.0, 4.0 );

var y = levy.quantile( 0.5 );
// returns ~10.792

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

var levy = new Levy( 2.0, 4.0 );

var mean = levy.mean;
// returns Infinity

var median = levy.median;
// returns ~10.792

var s2 = levy.variance;
// returns Infinity

var y = levy.cdf( 20.0 );
// returns ~0.637
```

</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-levy-ctor/main/LICENSE

[levy-distribution]: https://en.wikipedia.org/wiki/L%C3%A9vy_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

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

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

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

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

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

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