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Probability Density Function

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Rayleigh distribution probability density function (PDF).

The probability density function (PDF) for a Rayleigh random variable is

Probability density function (PDF) for a Rayleigh distribution.

where sigma > 0 is the scale parameter.


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


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

pdf( x, sigma )

Evaluates the probability density function for a Rayleigh distribution with scale parameter sigma.

var y = pdf( 0.3, 1.0 );
// returns ~0.287

y = pdf( 2.0, 0.8 );
// returns ~0.137

y = pdf( -1.0, 0.5 );
// returns 0.0

If provided NaN as any argument, the function returns NaN.

var y = pdf( NaN, 1.0 );
// returns NaN

y = pdf( 0.0, NaN );
// returns NaN

If provided sigma < 0, the function returns NaN.

var y = pdf( 2.0, -1.0 );
// returns NaN

If provided sigma = 0, the function evaluates the PDF of a degenerate distribution centered at 0.

var y = pdf( -2.0, 0.0 );
// returns 0.0

y = pdf( 0.0, 0.0 );
// returns Infinity

y = pdf( 2.0, 0.0 );
// returns 0.0

pdf.factory( sigma )

Returns a function for evaluating the probability density function (PDF) of a Rayleigh distribution with parameter sigma (scale parameter).

var myPDF = pdf.factory( 4.0 );

var y = myPDF( 6.0 );
// returns ~0.122

y = myPDF( 4.0 );
// returns ~0.152


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

var sigma;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    sigma = randu() * 10.0;
    y = pdf( x, sigma );
    console.log( 'x: %d, σ: %d, f(x;σ): %d', x.toFixed( 4 ), sigma.toFixed( 4 ), y.toFixed( 4 ) );


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.





Copyright © 2016-2023. The Stdlib Authors.




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