Kurtosis

Student's t distribution excess kurtosis.

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

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

Installation

npm install @stdlib/stats-base-dists-t-kurtosis

Usage

var kurtosis = require( '@stdlib/stats-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/stats-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 ) );
}

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.