README.md

About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

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Skewness

Fréchet distribution skewness.

The skewness for a Fréchet random variable shape α > 0, scale s > 0, and location parameter m is

$$\mathop{\mathrm{skew}} = \begin{cases} {\frac{\Gamma \left(1-{\frac{3}{\alpha }}\right)-3\Gamma \left(1-{\frac{2}{\alpha }}\right)\Gamma \left(1-{\frac{1}{\alpha }}\right)+2\Gamma^{3}\left(1-{\frac{1}{\alpha }}\right)}{{\sqrt{\left(\Gamma \left(1-{\frac{2}{\alpha }}\right)-\Gamma^{2}\left(1-{\frac{1}{\alpha }}\right)\right)^{3}}}}} & \text{ for }\alpha > 3\\\ \infty & \text{ otherwise }\end{cases}$$

where Γ is the gamma function.

Usage

import skewness from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-frechet-skewness@deno/mod.js';

skewness( alpha, s, m )

Returns the skewness for a Fréchet distribution with shape alpha > 0, scale s > 0, and location parameter m.

var y = skewness( 4.0, 1.0, 1.0 );
// returns ~5.605

y = skewness( 4.0, 8.0, -3.0 );
// returns ~5.605

y = skewness( 5.0, 1.0, 2.0 );
// returns ~3.535

If 0 < alpha <= 3, the function returns +Infinity.

var y = skewness( 2.5, 1.0, 1.0 );
// returns Infinity

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

var y = skewness( NaN, 1.0, -2.0 );
// returns NaN

y = skewness( 1.0, NaN, -2.0 );
// returns NaN

y = skewness( 1.0, 1.0, NaN );
// returns NaN

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

var y = skewness( 0.0, 3.0, 2.0 );
// returns NaN

y = skewness( -1.0, 3.0, 2.0 );
// returns NaN

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

var y = skewness( 1.0, 0.0, 2.0 );
// returns NaN

y = skewness( 1.0, -1.0, 2.0 );
// returns NaN

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@deno/mod.js';
import skewness from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-frechet-skewness@deno/mod.js';

var alpha;
var m;
var s;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    alpha = ( randu()*20.0 ) + EPS;
    s = ( randu()*20.0 ) + EPS;
    m = ( randu()*20.0 ) - 40.0;
    y = skewness( alpha, s, m );
    console.log( 'α: %d, s: %d, m: %d, skew(X;α,s,m): %d', alpha.toFixed( 4 ), s.toFixed( 4 ), m.toFixed( 4 ), y.toFixed( 4 ) );
}

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Notice

This package is part of stdlib, a standard library 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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.