Kurtosis

Fréchet distribution kurtosis.

The excess kurtosis for a Fréchet random variable shape α > 0, scale s > 0, and location parameter m is

where Γ is the gamma function.

Installation

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

Usage

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

kurtosis( alpha, s, m )

Returns the excess kurtosis for a Fréchet distribution with shape alpha > 0, scale s > 0, and location parameter m.

var y = kurtosis( 5.0, 1.0, 1.0 );
// returns ~45.092

y = kurtosis( 5.0, 10.0, 1.0 );
// returns ~45.092

y = kurtosis( 5.0, 1.0, 2.0 );
// returns ~45.092

If 0 < alpha <= 4, the function returns +Infinity.

var y = kurtosis( 2.5, 1.0, 1.0 );
// returns Infinity

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

var y = kurtosis( NaN, 1.0, -2.0 );
// returns NaN

y = kurtosis( 1.0, NaN, -2.0 );
// returns NaN

y = kurtosis( 1.0, 1.0, NaN );
// returns NaN

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

var y = kurtosis( 0.0, 3.0, 2.0 );
// returns NaN

y = kurtosis( 0.0, -1.0, 2.0 );
// returns NaN

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

var y = kurtosis( 1.0, 0.0, 2.0 );
// returns NaN

y = kurtosis( 1.0, -1.0, 2.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var kurtosis = require( '@stdlib/stats-base-dists-frechet-kurtosis' );

var alpha;
var m;
var s;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*20.0 ) + EPS;
    s = ( randu()*20.0 ) + EPS;
    m = ( randu()*40.0 ) - 20.0;
    y = kurtosis( alpha, s, m );
    console.log( 'α: %d, s: %d, m: %d, Kurt(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_frechet_kurtosis( alpha, s, m )

Returns the excess kurtosis for a Fréchet distribution with shape alpha, scale s, and location m.

double y = stdlib_base_dists_frechet_kurtosis( 5.0, 2.0, 0.0 );
// returns ~45.092

The function accepts the following arguments:

• alpha: [in] double shape parameter.
• s: [in] double scale parameter.
• m: [in] double location parameter.

double stdlib_base_dists_frechet_kurtosis( const double alpha, const double s, const double m );

Examples

#include "stdlib/stats/base/dists/frechet/kurtosis.h"
#include "stdlib/constants/float64/eps.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 alpha;
   double s;
   double m;
   double y;
   int i;

    for ( i = 0; i < 10; i++ ) {
       alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
       s = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
       m = random_uniform( -40.0, -20.0 );
       y = stdlib_base_dists_frechet_kurtosis( alpha, s, m );
       printf( "α: %.4lf, s: %.4lf, m: %.4lf, Kurt(X;α,s,m): %.4lf\n", alpha, s, m, 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.