Skewness

Chi-squared distribution skewness.

The skewness for a chi-squared random variable is

where k > 0 is the degrees of freedom.

Usage

var skewness = require( '@stdlib/stats/base/dists/chisquare/skewness' );

skewness( k )

Returns the skewness of a chi-squared distribution with degrees of freedom k.

var v = skewness( 9.0 );
// returns ~0.943

v = skewness( 0.5 );
// returns 4.0

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

var v = skewness( -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var skewness = require( '@stdlib/stats/base/dists/chisquare/skewness' );

var k;
var v;
var i;

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

C APIs

Usage

#include "stdlib/stats/base/dists/chisquare/skewness.h"

stdlib_base_dists_chisquare_skewness( k )

Evaluates the skewness of a chi-squared distribution with degrees of freedom k.

double out = stdlib_base_dists_chisquare_skewness( 9.0 );
// returns ~0.943

The function accepts the following arguments:

k: [in] double degrees of freedom.

double stdlib_base_dists_chisquare_skewness( const double k );

Examples

#include "stdlib/stats/base/dists/chisquare/skewness.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 k;
    double y;
    int i;

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