Skewness

Weibull distribution skewness.

The skewness for a Weibull random variable is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction normal upper Gamma left-parenthesis 1 plus 3 slash k right-parenthesis lamda cubed minus 3 mu sigma squared minus mu cubed Over sigma cubed EndFraction

where Γ is the gamma function, μ denotes the mean of the distribution, and σ the standard deviation.

Usage

var skewness = require( '@stdlib/math/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/math/float64-eps' );
var skewness = require( '@stdlib/math/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 ) );
}