Kurtosis

Weibull distribution excess kurtosis.

The excess kurtosis for a Weibull random variable with shape parameter λ > 0 and scale parameter k > 0 is

where Γ_i = Γ( 1 + i / k ).

Installation

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

Usage

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

kurtosis( k, lambda )

Returns the excess kurtosis of a Weibull distribution with shape parameter k and scale parameter lambda.

var v = kurtosis( 1.0, 1.0 );
// returns 6.0

v = kurtosis( 4.0, 12.0 );
// returns ~-0.252

v = kurtosis( 8.0, 2.0 );
// returns ~0.328

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

var v = kurtosis( NaN, 2.0 );
// returns NaN

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

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

var v = kurtosis( 0.0, 1.0 );
// returns NaN

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

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

var v = kurtosis( 1.0, 0.0 );
// returns NaN

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

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var kurtosis = require( '@stdlib/stats-base-dists-weibull-kurtosis' );

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, EPS, 10.0, opts );
var k = uniform( 10, EPS, 10.0, opts );

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

C APIs

Usage

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

stdlib_base_dists_weibull_kurtosis( k, lambda )

Returns the excess kurtosis of a Weibull distribution with shape parameter k and scale parameter lambda.

double out = stdlib_base_dists_weibull_kurtosis( 4.0, 12.0 );
// returns ~-0.252

The function accepts the following arguments:

• k: [in] double shape parameter.
• lambda: [in] double scale parameter.

double stdlib_base_dists_weibull_kurtosis( const double k, const double lambda );

Examples

#include "stdlib/stats/base/dists/weibull/kurtosis.h"
#include <stdlib.h>
#include <stdio.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 lambda;
    double k;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        k = random_uniform( 0.0, 10.0 );
        lambda = random_uniform( 0.0, 10.0 );
        y = stdlib_base_dists_weibull_kurtosis( k, lambda );
        printf( "k: %lf, λ: %lf, Kurt(X;k,λ): %lf\n", k, lambda, 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.