Kurtosis

Student's t distribution excess kurtosis.

The excess kurtosis for a Student's t random variable with degrees of freedom ν is

For ν smaller than two, the kurtosis is not defined.

Usage

var kurtosis = require( '@stdlib/stats/base/dists/t/kurtosis' );

kurtosis( v )

Returns the excess kurtosis of a Student's t distribution with degrees of freedom v.

var y = kurtosis( 9.0 );
// returns 1.2

y = kurtosis( 4.5 );
// returns 12.0

If provided 2 < v <= 4, the function returns infinity.

var y = kurtosis( 3.5 );
// returns Infinity

y = kurtosis( 2.9 );
// returns Infinity

y = kurtosis( 4.0 );
// returns Infinity

If provided v <= 2, the function returns NaN.

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

y = kurtosis( 0.8 );
// returns NaN

y = kurtosis( 2.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var kurtosis = require( '@stdlib/stats/base/dists/t/kurtosis' );

var v;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    v = randu() * 20.0;
    y = kurtosis( v );
    console.log( 'v: %d, Kurt(X,v): %d', v.toFixed( 4 ), y.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_t_kurtosis( v )

Returns the excess kurtosis of a Student's t distribution.

double out = stdlib_base_dists_t_kurtosis( 9.0 );
// returns 1.2

The function accepts the following arguments:

v: [in] double degrees of freedom.

double stdlib_base_dists_t_kurtosis( const double v );

Examples

#include "stdlib/stats/base/dists/t/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 v;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        v = random_uniform( 0.0, 20.0 );
        y = stdlib_base_dists_t_kurtosis( v );
        printf( "v: %lf, Kurt(X;v): %lf\n", v, y );
    }
}