Kurtosis

Chi distribution excess kurtosis.

The excess kurtosis for a chi random variable with degrees of freedom k is

where μ is the mean of the distribution, σ its standard deviation, and γ_1 the skewness.

Installation

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

Usage

var kurtosis = require( '@stdlib/stats-base-dists-chi-kurtosis' );

kurtosis( k )

Returns the excess kurtosis of a chi distribution with degrees of freedom k.

var v = kurtosis( 9.0 );
// returns ~0.011

v = kurtosis( 0.5 );
// returns ~2.534

If provided k <= 0, the function returns NaN.

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

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var kurtosis = require( '@stdlib/stats-base-dists-chi-kurtosis' );

var opts = {
    'dtype': 'float64'
};
var k = uniform( 10, 0.0, 20.0, opts );

logEachMap( 'k: %0.4f, Kurt(X;k): %0.4f', k, kurtosis );

C APIs

Usage

#include "stdlib/stats/base/dists/chi/kurtosis.h"

stdlib_base_dists_chi_kurtosis( k )

Returns the excess kurtosis of a chi distribution with degrees of freedom k.

double out = stdlib_base_dists_chi_kurtosis( 9.0 );
// returns ~0.011

The function accepts the following arguments:

• k: [in] double degrees of freedom.

double stdlib_base_dists_chi_kurtosis( const double k );

Examples

#include "stdlib/stats/base/dists/chi/kurtosis.h"
#include <stdio.h>
#include <stdlib.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v * ( max - min ) );
}

int main( void ) {
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        k = random_uniform( 1.0, 10.0 );
        y = stdlib_base_dists_chi_kurtosis( k );
        printf( "k: %lf, Kurt(X,k): %lf\n", k, y );
    }
}

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 © 2016-2026. The Stdlib Authors.