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.

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 );
    }
}