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Weibull distribution excess kurtosis.
The excess kurtosis for a Weibull random variable with shape parameter λ > 0 and scale parameter k > 0 is
where Γ_i = Γ( 1 + i / k ).
npm install @stdlib/stats-base-dists-weibull-kurtosisvar kurtosis = require( '@stdlib/stats-base-dists-weibull-kurtosis' );Returns the excess kurtosis of a Weibull distribution with shape parameter k and scale parameter lambda.
var v = kurtosis( 1.0, 1.0 );
// returns 6.0
v = kurtosis( 4.0, 12.0 );
// returns ~-0.252
v = kurtosis( 8.0, 2.0 );
// returns ~0.328If provided NaN as any argument, the function returns NaN.
var v = kurtosis( NaN, 2.0 );
// returns NaN
v = kurtosis( 2.0, NaN );
// returns NaNIf provided k <= 0, the function returns NaN.
var v = kurtosis( 0.0, 1.0 );
// returns NaN
v = kurtosis( -1.0, 1.0 );
// returns NaNIf provided lambda <= 0, the function returns NaN.
var v = kurtosis( 1.0, 0.0 );
// returns NaN
v = kurtosis( 1.0, -1.0 );
// returns NaNvar randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var kurtosis = require( '@stdlib/stats-base-dists-weibull-kurtosis' );
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 = kurtosis( k, lambda );
console.log( 'k: %d, λ: %d, Kurt(X;k,λ): %d', k.toFixed( 4 ), lambda.toFixed( 4 ), v.toFixed( 4 ) );
}This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
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