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Lévy

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

Lévy distribution constructor.

## Installation

bash
npm install @stdlib/stats-base-dists-levy-ctor

Alternatively,

- To load the package in a website via a script tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).
- If you are using Deno, visit the [deno][deno-url] branch (see [README][deno-readme] for usage intructions).
- For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [umd][umd-url] branch (see [README][umd-readme]).

The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

## 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

## Examples

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

*

## 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 © 2016-2025. The Stdlib [Authors][stdlib-authors].