Kurtosis

Rayleigh distribution excess kurtosis.

The excess kurtosis for a Rayleigh random variable is

upper K u r t left-parenthesis upper X right-parenthesis equals sigma StartRoot 2 ln left-parenthesis 2 right-parenthesis EndRoot

where σ > 0 is the scale parameter.

Usage

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

kurtosis( sigma )

Returns the excess kurtosis of a Rayleigh distribution with scale parameter sigma.

var y = kurtosis( 9.0 );
// returns ~0.245

y = kurtosis( 4.5 );
// returns ~0.245

If provided sigma < 0, the function returns NaN.

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

Examples

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

var sigma;
var y;
var i;

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