Skewness

Inverse gamma distribution skewness.

The skewness for an inverse gamma random variable with shape parameter α and rate parameter β is

s k e w left-parenthesis upper X right-parenthesis equals StartFraction 4 StartRoot alpha minus 2 EndRoot Over alpha minus 3 EndFraction

when α > 3. Otherwise, the skewness is not defined.

Usage

var skewness = require( '@stdlib/math/base/dists/invgamma/skewness' );

skewness( alpha, beta )

Returns the skewness of a inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var v = skewness( 4.0, 12.0 );
// returns ~5.657

v = skewness( 8.0, 2.0 );
// returns ~1.96

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( 2.0, 1.0 );
// 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/invgamma/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 ) );
}