Skewness

Chi distribution skewness.

The skewness for a chi random variable with degrees of freedom.k is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction mu Over sigma cubed EndFraction left-parenthesis 1 minus 2 sigma squared right-parenthesis

where μ is the mean of the distribution and σ its standard deviation.

Usage

var skewness = require( '@stdlib/math/base/dists/chi/skewness' );

skewness( k )

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

var v = skewness( 9.0 );
// returns ~0.252

v = skewness( 0.5 );
// returns ~1.544

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/math/base/dists/chi/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 ) );
}