Kurtosis

F distribution excess kurtosis.

The excess kurtosis for a F random variable with numerator degrees of freedom d1 and denominator degrees of freedom d2 is

for d1 > 0 and d2 > 8. Otherwise, the kurtosis is not defined.

Usage

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

kurtosis( d1, d2 )

Returns the excess kurtosis of an F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

var v = kurtosis( 4.0, 9.0 );
// returns ~114.273

v = kurtosis( 4.0, 12.0 );
// returns ~26.143

v = kurtosis( 8.0, 9.0 );
// returns ~100.167

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

var v = kurtosis( NaN, 7.0 );
// returns NaN

v = kurtosis( 3.0, NaN );
// returns NaN

If provided d1 <= 0, the function returns NaN.

var v = kurtosis( 0.0, 9.0 );
// returns NaN

v = kurtosis( -1.0, 9.0 );
// returns NaN

If provided d2 <= 8, the function returns NaN.

var v = kurtosis( 1.0, 8.0 );
// returns NaN

v = kurtosis( 2.2, 5.5 );
// returns NaN

v = kurtosis( 3.0, -1.0 );
// returns NaN

Examples

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

var d1;
var d2;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    d1 = ( randu()*10.0 ) + EPS;
    d2 = ( randu()*20.0 ) + EPS;
    v = kurtosis( d1, d2 );
    console.log( 'd1: %d, d2: %d, Kurt(X;d1,d2): %d', d1.toFixed( 4 ), d2.toFixed( 4 ), v.toFixed( 4 ) );
}

C APIs

Usage

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

stdlib_base_dists_f_kurtosis( d1, d2 )

Evaluates the excess kurtosis of an F distribution with parameters d1 (numerator degrees of freedom) and d2 (denominator degrees of freedom).

double out = stdlib_base_dists_f_kurtosis( 3.0, 9.0 );
// returns ~124.667

The function accepts the following arguments:

d1: [in] double numerator degrees of freedom.
d2: [in] double denominator degrees of freedom.

double stdlib_base_dists_f_kurtosis( const double d1, const double d2 );

Examples

#include "stdlib/stats/base/dists/f/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 d1;
    double d1;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        d1 = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        d1 = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_f_kurtosis( d1, d2 );
        printf( "d1: %lf, d2: %lf, Kurt(X;d1,d2): %lf\n", d1, d2, y );
    }
}