Kurtosis

Chi-squared distribution excess kurtosis.

The excess kurtosis for a chi-squared random variable is

upper K u r t left-parenthesis upper X right-parenthesis equals StartFraction 12 Over k EndFraction

where k > 0 is the degrees of freedom.

Usage

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

kurtosis( k )

Returns the excess kurtosis of a chi-squared distribution with degrees of freedom k.

var v = kurtosis( 9.0 );
// returns ~1.333

v = kurtosis( 0.5 );
// returns 24.0

If provided k <= 0, the function returns NaN.

var v = 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/chisquare/kurtosis' );

var k;
var v;
var i;

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