Skewness

Pareto (Type I) distribution skewness.

The skewness for a Pareto (Type I) random variable with shape parameter α and scale parameter β is

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

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

Usage

var skewness = require( '@stdlib/math/base/dists/pareto-type1/skewness' );

skewness( alpha, beta )

Returns the skewness of a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var v = skewness( 3.5, 1.0 );
// returns ~11.784

v = skewness( 4.0, 12.0 );
// returns ~7.071

v = skewness( 8.0, 2.0 );
// returns ~3.118

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 alpha <= 3, the function returns NaN.

var v = skewness( 3.0, 1.0 );
// returns NaN

v = skewness( 1.0, 3.0 );
// returns NaN

v = skewness( 0.0, 2.0 );
// returns NaN

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

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

var 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/pareto-type1/skewness' );

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

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*10.0 ) + EPS;
    beta = ( randu()*10.0 ) + 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 ) );
}