Kurtosis

Discrete uniform distribution excess kurtosis.

The excess kurtosis for a discrete uniform random variable with minimum support a and maximum support b is

where n = b - a + 1.

Installation

npm install @stdlib/stats-base-dists-discrete-uniform-kurtosis

Usage

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

kurtosis( a, b )

Returns the excess kurtosis of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var v = kurtosis( 0, 1 );
// returns -2.0

v = kurtosis( 4, 12 );
// returns ~-1.23

v = kurtosis( 2, 8 );
// returns ~-1.25

If a or b is not an integer value, the function returns NaN.

var v = kurtosis( 0.1, 2 );
// returns NaN

v = kurtosis( 0, 2.2 );
// returns NaN

v = kurtosis( NaN, 2 );
// returns NaN

v = kurtosis( 2, NaN );
// returns NaN

If provided a > b, the function returns NaN.

var v = kurtosis( 3, 2 );
// returns NaN

v = kurtosis( -1, -2 );
// returns NaN

Examples

var randint = require( '@stdlib/random-base-discrete-uniform' );
var kurtosis = require( '@stdlib/stats-base-dists-discrete-uniform-kurtosis' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randa();
    b = randb( a, a+randa() );
    v = kurtosis( a, b );
    console.log( 'a: %d, b: %d, Kurt(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

#include "stdlib/stats/base/dists/discrete-uniform/kurtosis.h"

stdlib_base_dists_discrete_uniform_kurtosis( a, b )

Returns the excess kurtosis of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

double out = stdlib_base_dists_discrete_uniform_kurtosis( 0, 1 );
// returns -2.0

The function accepts the following arguments:

• a: [in] int32_t minimum support.
• b: [in] int32_t maximum support.

double stdlib_base_dists_discrete_uniform_kurtosis( const int32_t a, const int32_t b );

Examples

#include "stdlib/stats/base/dists/discrete-uniform/kurtosis.h"
#include "stdlib/math/base/special/round.h"
#include <stdint.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 ) {
    int32_t a;
    int32_t b;
    double y;
    int i;

    for ( i = 0; i < 10; i++ ) {
        a = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
        b = stdlib_base_round( random_uniform( 0.0, 10.0 ) ) + a;
        y = stdlib_base_dists_discrete_uniform_kurtosis( a, b );
        printf( "a: %d, b: %d, Kurt(X;a,b): %lf\n", a, b, 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.