Kurtosis

Inverse gamma distribution excess kurtosis.

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

upper K u r t left-parenthesis upper X right-parenthesis equals StartFraction 30 alpha minus 66 Over left-parenthesis alpha minus 3 right-parenthesis left-parenthesis alpha minus 4 right-parenthesis EndFraction

when α > 4. Otherwise, the kurtosis is not defined.

Usage

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

kurtosis( alpha, beta )

Returns the excess kurtosis of an inverse gamma distribution with parameters alpha (shape parameter) and beta (rate parameter).

var v = kurtosis( 7.0, 5.0 );
// returns 12.0

v = kurtosis( 6.0, 12.0 );
// returns 19.0

v = kurtosis( 8.0, 2.0 );
// returns ~8.7

If provided NaN as any argument, the function returns NaN.

var v = kurtosis( NaN, 2.0 );
// returns NaN

v = kurtosis( 5.0, NaN );
// returns NaN

If provided alpha <= 4, the function returns NaN.

var v = kurtosis( 3.0, 1.0 );
// returns NaN

v = kurtosis( -1.0, 1.0 );
// returns NaN

If provided beta <= 0, the function returns NaN.

var v = kurtosis( 5.0, 0.0 );
// returns NaN

v = kurtosis( 5.0, -1.0 );
// returns NaN

Examples

var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/math/float64-eps' );
var kurtosis = require( '@stdlib/math/base/dists/invgamma/kurtosis' );

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 = kurtosis( alpha, beta );
    console.log( 'α: %d, β: %d, Kurt(X;α,β): %d', alpha.toFixed( 4 ), beta.toFixed( 4 ), v.toFixed( 4 ) );
}