Skewness

Beta prime distribution skewness.

The skewness for a beta prime random variable with first shape parameter α and second shape parameter β is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction 2 left-parenthesis 2 alpha plus beta minus 1 right-parenthesis Over beta minus 3 EndFraction StartRoot StartFraction beta minus 2 Over alpha left-parenthesis alpha plus beta minus 1 right-parenthesis EndFraction EndRoot

when α > 0 and β > 3. Otherwise, the skewness is not defined.

Usage

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

skewness( alpha, beta )

Returns the skewness of a beta prime distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var v = skewness( 2.0, 4.0 );
// returns ~6.261

v = skewness( 4.0, 12.0 );
// returns ~1.724

v = skewness( 8.0, 4.0 );
// returns ~5.729

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

var v = skewness( NaN, 4.0 );
// returns NaN

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

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

var v = skewness( 0.0, 4.0 );
// returns NaN

v = skewness( -1.0, 4.0 );
// returns NaN

If provided beta <= 3, the function returns NaN.

var v = skewness( 1.0, 2.5 );
// returns NaN

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

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

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var skewness = require( '@stdlib/math/base/dists/betaprime/skewness' );

var alpha;
var beta;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 3.0 + EPS;
    v = skewness( alpha, beta );
    console.log( 'α: %d, β: %d, skew(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}