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.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Skewness

Hypergeometric distribution skewness.

Imagine a scenario with a population of size N, of which a subpopulation of size K can be considered successes. We draw n observations from the total population. Defining the random variable X as the number of successes in the n draws, X is said to follow a hypergeometric distribution. The skewness for a hypergeometric random variable is

$$\mathop{\mathrm{skew}}\left( X \right) = \frac{(N-2K)(N-1)^{\frac{1}{2}}(N-2n)}{[nK(N-K)(N-n)]^{\frac{1}{2}}(N-2)}$$

Usage

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

skewness( N, K, n )

Returns the skewness of a hypergeometric distribution with parameters N (population size), K (subpopulation size), and n (number of draws).

var v = skewness( 16, 11, 4 );
// returns ~-0.258

v = skewness( 4, 2, 2 );
// returns 0.0

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

var v = skewness( NaN, 10, 4 );
// returns NaN

v = skewness( 20, NaN, 4 );
// returns NaN

v = skewness( 20, 10, NaN );
// returns NaN

If provided a population size N, subpopulation size K, or draws n which is not a nonnegative integer, the function returns NaN.

var v = skewness( 10.5, 5, 2 );
// returns NaN

v = skewness( 10, 1.5, 2 );
// returns NaN

v = skewness( 10, 5, -2.0 );
// returns NaN

If the number of draws n or the subpopulation size K exceed population size N, the function returns NaN.

var v = skewness( 10, 5, 12 );
// returns NaN

v = skewness( 10, 12, 5 );
// returns NaN

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import round from 'https://cdn.jsdelivr.net/gh/stdlib-js/math-base-special-round@deno/mod.js';
import skewness from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-hypergeometric-skewness@deno/mod.js';

var v;
var i;
var N;
var K;
var n;

for ( i = 0; i < 10; i++ ) {
    N = round( randu() * 20 );
    K = round( randu() * N );
    n = round( randu() * K );
    v = skewness( N, K, n );
    console.log( 'N: %d, K: %d, n: %d, skew(X;N,K,n): %d', N, K, n, v.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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Copyright

Copyright © 2016-2024. The Stdlib Authors.