Kurtosis

Discrete uniform distribution excess kurtosis.

The excess kurtosis for a discrete uniform random variable with minimum support a and maximum support b is

upper K u r t left-parenthesis upper X right-parenthesis equals minus StartFraction 6 left-parenthesis n squared plus 1 right-parenthesis Over 5 left-parenthesis n squared minus 1 right-parenthesis EndFraction

where n = b - a + 1.

Usage

var kurtosis = require( '@stdlib/math/base/dists/discrete-uniform/kurtosis' );

kurtosis( a, b )

Returns the excess kurtosis of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var v = kurtosis( 0, 1 );
// returns -2.0

v = kurtosis( 4, 12 );
// returns ~-1.23

v = kurtosis( 2, 8 );
// returns ~-1.25

If a or b is not an integer value, the function returns NaN.

var v = kurtosis( 0.1, 2 );
// returns NaN

v = kurtosis( 0, 2.2 );
// returns NaN

v = kurtosis( NaN, 2 );
// returns NaN

v = kurtosis( 2, NaN );
// returns NaN

If provided a > b, the function returns NaN.

var v = kurtosis( 3, 2 );
// returns NaN

v = kurtosis( -1, -2 );
// returns NaN

Examples

var randint = require( '@stdlib/random/base/discrete-uniform' );
var kurtosis = require( '@stdlib/math/base/dists/discrete-uniform/kurtosis' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var v;
var i;

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