Skewness
Pareto (Type I) distribution skewness.
The skewness for a Pareto (Type I) random variable with shape parameter α
and scale parameter β
is
for α > 3
and β > 0
. Otherwise, the skewness is not defined.
Usage
var skewness = require( '@stdlib/stats/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/float64/eps' );
var skewness = require( '@stdlib/stats/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 ) );
}