Skewness
The skewness for a Gumbel random variable with location μ and scale β is
where ζ is the Riemann zeta function.
Usage
var skewness = require( '@stdlib/stats/base/dists/gumbel/skewness' );
skewness( mu, beta )
Returns the skewness for a Gumbel distribution with location parameter mu and scale parameter beta.
var y = skewness( 2.0, 1.0 );
// returns ~1.14
y = skewness( 0.0, 1.0 );
// returns ~1.14
y = skewness( -1.0, 4.0 );
// returns ~1.14
If provided NaN as any argument, the function returns NaN.
var y = skewness( NaN, 1.0 );
// returns NaN
y = skewness( 0.0, NaN );
// returns NaN
If provided beta <= 0, the function returns NaN.
var y = skewness( 0.0, 0.0 );
// returns NaN
y = skewness( 0.0, -1.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var skewness = require( '@stdlib/stats/base/dists/gumbel/skewness' );
var beta;
var mu;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
mu = ( randu()*10.0 ) - 5.0;
beta = randu() * 20.0;
y = skewness( mu, beta );
console.log( 'µ: %d, β: %d, skew(X;µ,β): %d', mu.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}