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Rayleigh

Rayleigh distribution.

Installation

npm install @stdlib/stats-base-dists-rayleigh

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' );

rayleigh

Rayleigh distribution.

var dist = rayleigh;
// returns {...}

The namespace contains the following distribution functions:

• cdf( x, sigma ): Rayleigh distribution cumulative distribution function.
• logcdf( x, sigma ): Rayleigh distribution logarithm of cumulative distribution function.
• logpdf( x, sigma ): Rayleigh distribution logarithm of probability density function (PDF).
• mgf( t, sigma ): Rayleigh distribution moment-generating function (MGF).
• pdf( x, sigma ): Rayleigh distribution probability density function (PDF).
• quantile( p, sigma ): Rayleigh distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

• entropy( sigma ): Rayleigh distribution differential entropy.
• kurtosis( sigma ): Rayleigh distribution excess kurtosis.
• mean( sigma ): Rayleigh distribution expected value.
• median( sigma ): Rayleigh distribution median.
• mode( sigma ): Rayleigh distribution mode.
• skewness( sigma ): Rayleigh distribution skewness.
• stdev( sigma ): Rayleigh distribution standard deviation.
• variance( sigma ): Rayleigh distribution variance.

The namespace contains a constructor function for creating a Rayleigh distribution object.

• Rayleigh( [sigma] ): Rayleigh distribution constructor.

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

var dist = new Rayleigh( 2.0 );

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

Examples

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

/*
* The Rayleigh distribution can be used to model wind speeds.
* Let's consider a scenario where we want to estimate various properties related to wind speeds.
*/

// Set the Rayleigh distribution parameter (scale parameter):
var s = 10.0;

// Calculate mean, variance, and standard deviation of the Rayleigh distribution:
console.log( rayleigh.mean( s ) );
// => ~12.533

console.log( rayleigh.variance( s ) );
// => ~42.920

console.log( rayleigh.stdev( s ) );
// => ~6.551

// Evaluate the Probability Density Function (PDF) for a specific wind speed:
var w = 15.0;
console.log( rayleigh.pdf( w, s ) );
// => ~0.049

// Determine Cumulative Distribution Function (CDF) for wind speeds up to a certain value:
var t = 15.0;
console.log( rayleigh.cdf( t, s ) );
// => ~0.675

// Calculate the probability of wind speeds exceeding the threshold:
var p = 1.0 - rayleigh.cdf( t, s );
console.log( 'Probability of wind speeds exceeding ' + t + ' m/s:', p );

// Find the wind speed at which there's a 70% chance it won't exceed using the Quantile function:
var c = 0.7;
console.log( rayleigh.quantile( c, s ) );
// => ~15.518

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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.