Probability Density Function

Rayleigh distribution probability density function (PDF).

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

where sigma > 0 is the scale parameter.

Installation

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

Usage

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

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pdf = require( '@stdlib/stats-base-dists-rayleigh-pdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, 0.0, 10.0, opts );
var sigma = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, σ: %0.4f, f(x;σ): %0.4f', x, sigma, pdf );

C APIs

Usage

#include "stdlib/stats/base/dists/rayleigh/pdf.h"

stdlib_base_dists_rayleigh_pdf( x, sigma )

Evaluates the probability density function (PDF) for a Rayleigh distribution.

double out = stdlib_base_dists_rayleigh_pdf( 0.3, 1.0 );
// returns ~0.287

The function accepts the following arguments:

• x: [in] double input value.
• sigma: [in] double scale parameter.

double stdlib_base_dists_rayleigh_pdf( const double x, const double sigma );

Examples

#include "stdlib/stats/base/dists/rayleigh/pdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double sigma;
    double x;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( 0.0, 10.0 );
        sigma = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_rayleigh_pdf( x, sigma );
        printf( "x: %lf, σ: %lf, f(x;σ): %lf\n", x, sigma, y );
    }
}

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.