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Rayleigh

Rayleigh distribution constructor.

Installation

npm install @stdlib/stats-base-dists-rayleigh-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 Rayleigh = require( '@stdlib/stats-base-dists-rayleigh-ctor' );

Rayleigh( [sigma] )

Returns an Rayleigh distribution object.

var rayleigh = new Rayleigh();

var mu = rayleigh.mean;
// returns ~1.253

By default, sigma = 1.0. To create a distribution having a different scale parameter sigma, provide a parameter value.

var rayleigh = new Rayleigh( 4.0 );

var mu = rayleigh.mean;
// returns ~5.013

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rayleigh

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

Writable Properties

rayleigh.sigma

Scale parameter of the distribution. sigma must be a positive number.

var rayleigh = new Rayleigh( 2.0 );

var sigma = rayleigh.sigma;
// returns 2.0

rayleigh.sigma = 3.0;

sigma = rayleigh.sigma;
// returns 3.0

---

Computed Properties

Rayleigh.prototype.entropy

Returns the differential entropy.

var rayleigh = new Rayleigh( 4.0 );

var entropy = rayleigh.entropy;
// returns ~2.328

Rayleigh.prototype.kurtosis

Returns the excess kurtosis.

var rayleigh = new Rayleigh( 4.0 );

var kurtosis = rayleigh.kurtosis;
// returns ~0.245

Rayleigh.prototype.mean

Returns the median.

var rayleigh = new Rayleigh( 4.0 );

var mu = rayleigh.mean;
// returns ~5.013

Rayleigh.prototype.median

Returns the median.

var rayleigh = new Rayleigh( 4.0 );

var median = rayleigh.median;
// returns ~4.71

Rayleigh.prototype.mode

Returns the mode.

var rayleigh = new Rayleigh( 4.0 );

var mode = rayleigh.mode;
// returns 4.0

Rayleigh.prototype.skewness

Returns the skewness.

var rayleigh = new Rayleigh( 4.0 );

var skewness = rayleigh.skewness;
// returns ~0.631

Rayleigh.prototype.stdev

Returns the standard deviation.

var rayleigh = new Rayleigh( 4.0 );

var s = rayleigh.stdev;
// returns ~2.62

Rayleigh.prototype.variance

Returns the variance.

var rayleigh = new Rayleigh( 4.0 );

var s2 = rayleigh.variance;
// returns ~6.867

---

Methods

Rayleigh.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.cdf( 1.5 );
// returns ~0.245

Rayleigh.prototype.logcdf( x )

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

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.logcdf( 1.5 );
// returns ~-1.406

Rayleigh.prototype.logpdf( x )

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

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.logpdf( 0.8 );
// returns ~-1.689

Rayleigh.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.mgf( 0.5 );
// returns ~5.586

Rayleigh.prototype.pdf( x )

Evaluates the probability density function (PDF).

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.pdf( 0.8 );
// returns ~0.185

Rayleigh.prototype.quantile( p )

Evaluates the quantile function at probability p.

var rayleigh = new Rayleigh( 2.0 );

var y = rayleigh.quantile( 0.5 );
// returns ~2.355

y = rayleigh.quantile( 1.9 );
// returns NaN

---

Examples

var Rayleigh = require( '@stdlib/stats-base-dists-rayleigh-ctor' );

var rayleigh = new Rayleigh( 2.0, 4.0 );

var mu = rayleigh.mean;
// returns ~2.507

var mode = rayleigh.mode;
// returns 2.0

var s2 = rayleigh.variance;
// returns ~1.717

var y = rayleigh.cdf( 0.8 );
// returns ~0.077

---

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.