Skewness

Rayleigh distribution skewness.

The skewness for a Rayleigh random variable is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction 2 StartRoot pi EndRoot left-parenthesis pi minus 3 right-parenthesis Over left-parenthesis 4 minus pi right-parenthesis Superscript 3 slash 2 Baseline EndFraction

where σ > 0 is the scale parameter.

Usage

var skewness = require( '@stdlib/math/base/dists/rayleigh/skewness' );

skewness( sigma )

Returns the skewness of a Rayleigh distribution with scale parameter sigma.

var y = skewness( 9.0 );
// returns ~0.631

y = skewness( 3.5 );
// returns ~0.631

If provided sigma < 0, the function returns NaN.

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

Examples

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

var sigma;
var y;
var i;

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