Skewness
The skewness for a Weibull random variable is
where Γ is the gamma function, μ denotes the mean of the distribution, and σ the standard deviation.
Usage
var skewness = require( '@stdlib/stats/base/dists/weibull/skewness' );
skewness( k, lambda )
Returns the skewness of a Weibull distribution with parameters k (shape parameter) and lambda (scale parameter).
var v = skewness( 1.0, 1.0 );
// returns 2.0
v = skewness( 4.0, 12.0 );
// returns ~-0.087
v = skewness( 8.0, 2.0 );
// returns ~-0.534
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 k <= 0, the function returns NaN.
var v = skewness( 0.0, 1.0 );
// returns NaN
v = skewness( -1.0, 1.0 );
// returns NaN
If provided lambda <= 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/weibull/skewness' );
var lambda;
var k;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
k = ( randu()*10.0 ) + EPS;
lambda = ( randu()*10.0 ) + EPS;
v = skewness( k, lambda );
console.log( 'k: %d, λ: %d, skew(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}