Variance

Rayleigh distribution variance.

The variance for a Rayleigh random variable is

upper V a r left-parenthesis upper X right-parenthesis equals StartFraction 4 minus pi Over 2 EndFraction sigma squared

where σ > 0 is the scale parameter.

Usage

var variance = require( '@stdlib/math/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/math/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 ) );
}