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Lévy

Lévy distribution constructor.

Installation

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 available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

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

Levy( [mu, c] )

Returns a Lévy distribution object.

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.

var levy = new Levy( 2.0, 4.0 );

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

---

levy

A Lévy distribution object has the following properties and methods...

Writable Properties

levy.mu

Location parameter of the distribution.

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.

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.

var levy = new Levy( 4.0, 12.0 );

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

Levy.prototype.mean

Returns the expected value.

var levy = new Levy( 4.0, 12.0 );

var mu = levy.mean;
// returns Infinity

Levy.prototype.median

Returns the median.

var levy = new Levy( 4.0, 12.0 );

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

Levy.prototype.mode

Returns the mode.

var levy = new Levy( 4.0, 12.0 );

var mode = levy.mode;
// returns 8.0

Levy.prototype.stdev

Returns the standard deviation.

var levy = new Levy( 4.0, 12.0 );

var s = levy.stdev;
// returns Infinity

Levy.prototype.variance

Returns the variance.

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).

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).

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).

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).

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 at probability p.

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

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, 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, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.