Skewness

Pareto (Type I) distribution skewness.

The skewness for a Pareto (Type I) random variable with shape parameter α and scale parameter β is

for α > 3 and β > 0. Otherwise, the skewness is not defined.

Installation

npm install @stdlib/stats-base-dists-pareto-type1-skewness

Usage

var skewness = require( '@stdlib/stats-base-dists-pareto-type1-skewness' );

skewness( alpha, beta )

Returns the skewness of a Pareto (Type I) distribution with parameters alpha (shape parameter) and beta (scale parameter).

var v = skewness( 3.5, 1.0 );
// returns ~11.784

v = skewness( 4.0, 12.0 );
// returns ~7.071

v = skewness( 8.0, 2.0 );
// returns ~3.118

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

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

v = skewness( 2.0, NaN );
// returns NaN

If provided alpha <= 3, the function returns NaN.

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

v = skewness( 1.0, 3.0 );
// returns NaN

v = skewness( 0.0, 2.0 );
// returns NaN

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

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

var v = skewness( 1.0, 0.0 );
// returns NaN

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

Examples

var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var skewness = require( '@stdlib/stats-base-dists-pareto-type1-skewness' );

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 = skewness( alpha, beta );
    console.log( 'α: %d, β: %d, skew(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.