Kurtosis

Geometric distribution excess kurtosis.

The excess kurtosis for a geometric random variable is

upper K u r t left-parenthesis upper X right-parenthesis equals 6 plus StartFraction p squared Over 1 minus p EndFraction

where p is the success probability.

Usage

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

kurtosis( p )

Returns the excess kurtosis of a geometric distribution with success probability p.

var v = kurtosis( 0.1 );
// returns ~6.011

v = kurtosis( 0.5 );
// returns 6.5

If provided a success probability p outside of [0,1], the function returns NaN.

var v = kurtosis( NaN );
// returns NaN

v = kurtosis( 1.5 );
// returns NaN

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/geometric/kurtosis' );

var v;
var i;
var p;

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