Kurtosis

Binomial distribution excess kurtosis.

The excess kurtosis for a binomial random variable is

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

where n is the number of trials and p is the success probability.

Usage

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

kurtosis( n, p )

Returns the excess kurtosis of a binomial distribution with number of trials n and success probability p.

var v = kurtosis( 20, 0.1 );
// returns ~0.256

v = kurtosis( 50, 0.5 );
// returns ~-0.04

If provided NaN as any argument, the function returns NaN.

var v = kurtosis( NaN, 0.5 );
// returns NaN

v = kurtosis( 20, NaN );
// returns NaN

If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

var v = kurtosis( 1.5, 0.5 );
// returns NaN

v = kurtosis( -2.0, 0.5 );
// returns NaN

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

var v = kurtosis( 20, -1.0 );
// returns NaN

v = kurtosis( 20, 1.5 );
// 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/binomial/kurtosis' );

var v;
var i;
var n;
var p;

for ( i = 0; i < 10; i++ ) {
    n = round( randu() * 100.0 );
    p = randu();
    v = kurtosis( n, p );
    console.log( 'n: %d, p: %d, Kurt(X;n,p): %d', n, p.toFixed( 4 ), v.toFixed( 4 ) );
}