Cumulative Distribution Function

Rayleigh distribution cumulative distribution function.

The cumulative distribution function for a Rayleigh random variable is

where sigma > 0 is the scale parameter.

Installation

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

Usage

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

cdf( x, sigma )

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

var y = cdf( 2.0, 3.0 );
// returns ~0.199

y = cdf( 1.0, 2.0 );
// returns ~0.118

y = cdf( -1.0, 4.0 );
// returns 0.0

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

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

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

If provided sigma < 0, the function returns NaN.

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

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

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

y = cdf( 0.0, 0.0 );
// returns 1.0

y = cdf( 2.0, 0.0 );
// returns 1.0

cdf.factory( sigma )

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

var myCDF = cdf.factory( 0.5 );
var y = myCDF( 1.0 );
// returns ~0.865

y = myCDF( 0.5 );
// returns ~0.393

Examples

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

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, cdf );

C APIs

Usage

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

stdlib_base_dists_rayleigh_cdf( x, sigma )

Evaluates the cumulative distribution function (CDF) for a Rayleigh distribution.

double out = stdlib_base_dists_rayleigh_cdf( 2.0, 3.0 );
// returns ~0.199

The function accepts the following arguments:

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

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

Examples

#include "stdlib/stats/base/dists/rayleigh/cdf.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_cdf( 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.