Skewness

Kumaraswamy's double bounded distribution skewness.

The skewness for a Kumaraswamy's double bounded random variable with first shape parameter a and second shape parameter b is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction m 3 minus 3 m 1 sigma squared minus m 1 cubed Over left-parenthesis sigma squared right-parenthesis Superscript 3 slash 2 Baseline EndFraction

where σ^2 is the variance and the raw moments of the distribution are given by

m Subscript n Baseline equals b upper B left-parenthesis 1 plus StartFraction n Over a EndFraction comma b right-parenthesis

with B denoting the beta function.

Usage

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

skewness( a, b )

Returns the skewness of a Kumaraswamy's double bounded distribution with first shape parameter a and second shape parameter b.

var v = skewness( 1.0, 1.0 );
// returns 0.0

v = skewness( 4.0, 12.0 );
// returns ~-0.201

v = skewness( 2.0, 8.0 );
// returns ~0.384

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

var v = skewness( NaN, 2.0 );
// returns NaN

v = skewness( 2.0, NaN );
// returns NaN

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

var y = skewness( -1.0, 0.5 );
// returns NaN

y = skewness( 0.0, 0.5 );
// returns NaN

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

var y = skewness( 0.5, -1.0 );
// returns NaN

y = skewness( 0.5, 0.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var skewness = require( '@stdlib/math/base/dists/kumaraswamy/skewness' );

var a;
var b;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    a = randu() * 10.0;
    b = randu() * 10.0;
    v = skewness( a, b );
    console.log( 'a: %d, b: %d, skew(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}