Ecosyste.ms: Awesome

An open API service indexing awesome lists of open source software.

Awesome Lists | Featured Topics | Projects

https://github.com/stdlib-js/stats-incr-skewness

Compute a corrected sample skewness incrementally.
https://github.com/stdlib-js/stats-incr-skewness

accumulator corrected incremental javascript math mathematics node node-js nodejs sample-skewness shape skewness statistics stats stdlib

Last synced: 2 months ago
JSON representation

Compute a corrected sample skewness incrementally.

Awesome Lists containing this project

README 

        



  

    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!



# incrskewness



[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] 



> Compute a [corrected sample skewness][sample-skewness] incrementally.



The [skewness][sample-skewness] for a random variable `X` is defined as



```math

\mathop{\mathrm{Skewness}}[X] = \mathrm{E}\biggl[ \biggl( \frac{X - \mu}{\sigma} \biggr)^3 \biggr]

```



For a sample of `n` values, the [sample skewness][sample-skewness] is



```math

b_1 = \frac{m_3}{s^3} = \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}

```



where `m_3` is the sample third central moment and `s` is the sample standard deviation.



An alternative definition for the [sample skewness][sample-skewness] which includes an adjustment factor (and is the implemented definition) is



```math

G_1 = \frac{n^2}{(n-1)(n-2)} \frac{m_3}{s^3} = \frac{\sqrt{n(n-1)}}{n-2} \frac{\frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^3}{\biggl( \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \bar{x})^2 \biggr)^{3/2}}

```



## Installation



```bash

npm install @stdlib/stats-incr-skewness

```



Alternatively,



-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).

-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).

-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).



The [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.



To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.



## Usage



```javascript

var incrskewness = require( '@stdlib/stats-incr-skewness' );

```



#### incrskewness()



Returns an accumulator `function` which incrementally computes a [corrected sample skewness][sample-skewness].



```javascript

var accumulator = incrskewness();

```



#### accumulator( \[x] )



If provided an input value `x`, the accumulator function returns an updated [corrected sample skewness][sample-skewness]. If not provided an input value `x`, the accumulator function returns the current [corrected sample skewness][sample-skewness].



```javascript

var accumulator = incrskewness();



var skewness = accumulator();

// returns null



skewness = accumulator( 2.0 );

// returns null



skewness = accumulator( -5.0 );

// returns null



skewness = accumulator( -10.0 );

// returns ~0.492



skewness = accumulator();

// returns ~0.492

```



## Notes



-   Input values are **not** type checked. If provided `NaN` or a value which, when used in computations, results in `NaN`, the accumulated value is `NaN` for **all** future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly **before** passing the value to the accumulator function.



## Examples



```javascript

var randu = require( '@stdlib/random-base-randu' );

var incrskewness = require( '@stdlib/stats-incr-skewness' );



var accumulator;

var v;

var i;



// Initialize an accumulator:

accumulator = incrskewness();



// For each simulated datum, update the corrected sample skewness...

for ( i = 0; i < 100; i++ ) {

    v = randu() * 100.0;

    accumulator( v );

}

console.log( accumulator() );

```



* * *



## References



-   Joanes, D. N., and C. A. Gill. 1998. "Comparing measures of sample skewness and kurtosis." _Journal of the Royal Statistical Society: Series D (The Statistician)_ 47 (1). Blackwell Publishers Ltd: 183–89. doi:[10.1111/1467-9884.00122][@joanes:1998].



* * *



## See Also



-   [`@stdlib/stats-incr/kurtosis`][@stdlib/stats/incr/kurtosis]: compute a corrected sample excess kurtosis incrementally.

-   [`@stdlib/stats-incr/mean`][@stdlib/stats/incr/mean]: compute an arithmetic mean incrementally.

-   [`@stdlib/stats-incr/stdev`][@stdlib/stats/incr/stdev]: compute a corrected sample standard deviation incrementally.

-   [`@stdlib/stats-incr/summary`][@stdlib/stats/incr/summary]: compute a statistical summary incrementally.

-   [`@stdlib/stats-incr/variance`][@stdlib/stats/incr/variance]: compute an unbiased sample variance incrementally.



* * *



## Notice



This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].



#### Community



[![Chat][chat-image]][chat-url]



---



## License



See [LICENSE][stdlib-license].



## Copyright



Copyright © 2016-2024. The Stdlib [Authors][stdlib-authors].



[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-incr-skewness.svg

[npm-url]: https://npmjs.org/package/@stdlib/stats-incr-skewness



[test-image]: https://github.com/stdlib-js/stats-incr-skewness/actions/workflows/test.yml/badge.svg?branch=main

[test-url]: https://github.com/stdlib-js/stats-incr-skewness/actions/workflows/test.yml?query=branch:main



[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-incr-skewness/main.svg

[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-skewness?branch=main



[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg

[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im



[stdlib]: https://github.com/stdlib-js/stdlib



[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors



[umd]: https://github.com/umdjs/umd

[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules



[deno-url]: https://github.com/stdlib-js/stats-incr-skewness/tree/deno

[deno-readme]: https://github.com/stdlib-js/stats-incr-skewness/blob/deno/README.md

[umd-url]: https://github.com/stdlib-js/stats-incr-skewness/tree/umd

[umd-readme]: https://github.com/stdlib-js/stats-incr-skewness/blob/umd/README.md

[esm-url]: https://github.com/stdlib-js/stats-incr-skewness/tree/esm

[esm-readme]: https://github.com/stdlib-js/stats-incr-skewness/blob/esm/README.md

[branches-url]: https://github.com/stdlib-js/stats-incr-skewness/blob/main/branches.md



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-skewness/main/LICENSE



[sample-skewness]: https://en.wikipedia.org/wiki/Skewness



[@joanes:1998]: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/



[@stdlib/stats/incr/kurtosis]: https://github.com/stdlib-js/stats-incr-kurtosis



[@stdlib/stats/incr/mean]: https://github.com/stdlib-js/stats-incr-mean



[@stdlib/stats/incr/stdev]: https://github.com/stdlib-js/stats-incr-stdev



[@stdlib/stats/incr/summary]: https://github.com/stdlib-js/stats-incr-summary



[@stdlib/stats/incr/variance]: https://github.com/stdlib-js/stats-incr-variance