Kurtosis

Student's t distribution excess kurtosis.

The excess kurtosis for a Student's t random variable with degrees of freedom ν is

upper K u r t left-parenthesis upper X right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column StartFraction 6 Over nu minus 4 EndFraction 2nd Column for nu greater-than 2 2nd Row 1st Column normal infinity 2nd Column for 2 less-than nu less-than-or-equal-to 4 EndLayout

For ν smaller than two, the kurtosis is not defined.

Usage

var kurtosis = require( '@stdlib/math/base/dists/t/kurtosis' );

kurtosis( v )

Returns the excess kurtosis of a Student's t distribution with degrees of freedom v.

var y = kurtosis( 9.0 );
// returns 1.2

y = kurtosis( 4.5 );
// returns 12.0

If provided 2 < v <= 4, the function returns infinity.

var y = kurtosis( 3.5 );
// returns Infinity

y = kurtosis( 2.9 );
// returns Infinity

y = kurtosis( 4.0 );
// returns Infinity

If provided v <= 2, the function returns NaN.

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

y = kurtosis( 0.8 );
// returns NaN

y = kurtosis( 2.0 );
// 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/t/kurtosis' );

var v;
var y;
var i;

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