Variance

Rayleigh distribution variance.

The variance for a Rayleigh random variable is

where σ > 0 is the scale parameter.

Usage

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

variance( sigma )

Returns the variance of a Rayleigh distribution with scale sigma.

var y = variance( 9.0 );
// returns ~34.765

y = variance( 3.5 );
// returns ~5.258

If provided sigma < 0, the function returns NaN.

var y = variance( -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var variance = require( '@stdlib/stats/base/dists/rayleigh/variance' );

var sigma;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    sigma = randu() * 20.0;
    y = variance( sigma );
    console.log( 'σ: %d, Var(X,σ): %d', sigma.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_rayleigh_variance( sigma )

Returns the variance of a Rayleigh distribution.

double out = stdlib_base_dists_rayleigh_variance( 9.0 );
// returns ~34.765

The function accepts the following arguments:

sigma: [in] double scale parameter.

double stdlib_base_dists_rayleigh_variance( const double sigma );

Examples

#include "stdlib/stats/base/dists/rayleigh/variance.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 y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        sigma = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_rayleigh_variance( sigma );
        printf( "σ: %lf, Var(X;σ): %lf\n", sigma, y );
    }
}