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Kumaraswamy's double bounded distribution excess kurtosis.
The excess kurtosis for a Kumaraswamy's double bounded random variable with first shape parameter a
and second shape parameter b
is
where the raw moments of the distribution are given by
with B
denoting the beta function.
import kurtosis from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-kumaraswamy-kurtosis@deno/mod.js';
Returns the excess kurtosis of a Kumaraswamy's double bounded distribution with first shape parameter a
and second shape parameter b
.
var v = kurtosis( 1.0, 1.0 );
// returns ~1.8
v = kurtosis( 4.0, 12.0 );
// returns ~2.704
v = kurtosis( 2.0, 8.0 );
// returns ~2.666
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 a <= 0
, the function returns NaN
.
var y = kurtosis( -1.0, 0.5 );
// returns NaN
y = kurtosis( 0.0, 0.5 );
// returns NaN
If provided b <= 0
, the function returns NaN
.
var y = kurtosis( 0.5, -1.0 );
// returns NaN
y = kurtosis( 0.5, 0.0 );
// returns NaN
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import kurtosis from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-kumaraswamy-kurtosis@deno/mod.js';
var a;
var b;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
a = randu() * 10.0;
b = randu() * 10.0;
v = kurtosis( a, b );
console.log( 'a: %d, b: %d, Kurt(X;a,b): %d', a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}
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