Kurtosis
Gamma distribution excess kurtosis.
The excess kurtosis for a gamma random variable with shape parameter α > 0
and rate parameter β > 0
is
Usage
var kurtosis = require( '@stdlib/stats/base/dists/gamma/kurtosis' );
kurtosis( alpha, beta )
Returns the excess kurtosis of a gamma distribution with parameters alpha
(shape parameter) and beta
(rate parameter).
var v = kurtosis( 1.0, 1.0 );
// returns 6.0
v = kurtosis( 4.0, 12.0 );
// returns 1.5
v = kurtosis( 8.0, 2.0 );
// returns 0.75
If provided NaN
as any argument, the function returns NaN
.
var v = kurtosis( NaN, 2.0 );
// returns NaN
v = kurtosis( 2.0, NaN );
// returns NaN
If provided alpha <= 0
, the function returns NaN
.
var v = kurtosis( 0.0, 1.0 );
// returns NaN
v = kurtosis( -1.0, 1.0 );
// returns NaN
If provided beta <= 0
, the function returns NaN
.
var v = kurtosis( 1.0, 0.0 );
// returns NaN
v = kurtosis( 1.0, -1.0 );
// returns NaN
Examples
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var kurtosis = require( '@stdlib/stats/base/dists/gamma/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 ) );
}