@stdlib/stats-base-dists-pareto-type1-kurtosis
v0.2.2
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Pareto (Type I) distribution excess kurtosis.
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Kurtosis
Pareto (Type I) distribution excess kurtosis.
The excess kurtosis for a Pareto (Type I) random variable with shape parameter α
and scale parameter β
is
for α > 4
and β > 0
. Otherwise, the kurtosis is not defined.
Installation
npm install @stdlib/stats-base-dists-pareto-type1-kurtosis
Usage
var kurtosis = require( '@stdlib/stats-base-dists-pareto-type1-kurtosis' );
kurtosis( alpha, beta )
Returns the excess kurtosis of a Pareto (Type I) distribution with parameters alpha
(shape parameter) and beta
(scale parameter).
var v = kurtosis( 5.0, 1.0 );
// returns ~70.8
v = kurtosis( 4.5, 12.0 );
// returns ~146.444
v = kurtosis( 8.0, 2.0 );
// returns ~19.725
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 <= 4
, the function returns NaN
.
var v = kurtosis( 0.0, 1.0 );
// returns NaN
v = kurtosis( 3.0, 1.0 );
// returns NaN
v = kurtosis( 4.0, 2.0 );
// 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-pareto-type1-kurtosis' );
var alpha;
var beta;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
alpha = ( randu()*10.0 ) + 4.0 + 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 ) );
}
Notice
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.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 2016-2024. The Stdlib Authors.