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

Compute an exponentially weighted variance incrementally.
https://github.com/stdlib-js/stats-incr-ewvariance

accumulator deviation dispersion emv ewmv exponential incremental javascript math mathematics node node-js nodejs statistics stats stdlib var variance weighted

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Compute an exponentially weighted variance incrementally.

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README 

        



  

    About stdlib...

  

  
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# increwvariance



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



> Compute an [exponentially weighted variance][moving-average] incrementally.



An [exponentially weighted variance][moving-average] can be defined recursively as



```math

S_n = \begin{cases} 0 & \textrm{if}\ n = 0 \\ (1 - \alpha) (S_{n-1} + \alpha(x_n - \mu_{n-1})^2) & \textrm{if}\ n > 0 \end{cases}

```



where `μ` is the [exponentially weighted mean][@stdlib/stats/incr/ewmean].



## Installation



```bash

npm install @stdlib/stats-incr-ewvariance

```



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 increwvariance = require( '@stdlib/stats-incr-ewvariance' );

```



#### increwvariance( alpha )



Returns an accumulator `function` which incrementally computes an [exponentially weighted variance][moving-average], where `alpha` is a smoothing factor between `0` and `1`.



```javascript

var accumulator = increwvariance( 0.5 );

```



#### accumulator( \[x] )



If provided an input value `x`, the accumulator function returns an updated variance. If not provided an input value `x`, the accumulator function returns the current variance.



```javascript

var accumulator = increwvariance( 0.5 );



var v = accumulator();

// returns null



v = accumulator( 2.0 );

// returns 0.0



v = accumulator( 1.0 );

// returns 0.25



v = accumulator( 3.0 );

// returns 0.6875



v = accumulator();

// returns 0.6875

```



## 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 increwvariance = require( '@stdlib/stats-incr-ewvariance' );



var accumulator;

var v;

var i;



// Initialize an accumulator:

accumulator = increwvariance( 0.5 );



// For each simulated datum, update the exponentially weighted variance...

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

    v = randu() * 100.0;

    accumulator( v );

}

console.log( accumulator() );

```



* * *



## See Also



-   [`@stdlib/stats-incr/ewmean`][@stdlib/stats/incr/ewmean]: compute an exponentially weighted mean incrementally.

-   [`@stdlib/stats-incr/ewstdev`][@stdlib/stats/incr/ewstdev]: compute an exponentially weighted standard deviation incrementally.

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

-   [`@stdlib/stats-incr/mvariance`][@stdlib/stats/incr/mvariance]: compute a moving 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-ewvariance.svg

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



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

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



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

[coverage-url]: https://codecov.io/github/stdlib-js/stats-incr-ewvariance?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-ewvariance/tree/deno

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

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

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

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

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

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



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



[moving-average]: https://en.wikipedia.org/wiki/Moving_average



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



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



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



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