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

Compute a moving arithmetic mean and corrected sample standard deviation incrementally.
https://github.com/stdlib-js/stats-incr-mmeanstdev

arithmetic-mean average avg central-tendency javascript math mathematics mean moving-average moving-mean node node-js nodejs sample sample-variance statistics stats stdlib unbiased variance

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Compute a moving arithmetic mean and corrected sample standard deviation incrementally.

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README 

        



  

    About stdlib...

  

  
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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!



# incrmmeanstdev



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



> Compute a moving [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][standard-deviation] incrementally.



For a window of size `W`, the [arithmetic mean][arithmetic-mean] is defined as



```math

\bar{x} = \frac{1}{W} \sum_{i=0}^{W-1} x_i

```



and the [corrected sample standard deviation][standard-deviation] is defined as



```math

s = \sqrt{\frac{1}{W-1} \sum_{i=0}^{W-1} ( x_i - \bar{x} )^2}

```



## Installation



```bash

npm install @stdlib/stats-incr-mmeanstdev

```



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 incrmmeanstdev = require( '@stdlib/stats-incr-mmeanstdev' );

```



#### incrmmeanstdev( \[out,] window )



Returns an accumulator `function` which incrementally computes a moving [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][standard-deviation]. The `window` parameter defines the number of values over which to compute the moving [arithmetic mean][arithmetic-mean] and [corrected sample standard deviation][standard-deviation].



```javascript

var accumulator = incrmmeanstdev( 3 );

```



By default, the returned accumulator `function` returns the accumulated values as a two-element `array`. To avoid unnecessary memory allocation, the function supports providing an output (destination) object.



```javascript

var Float64Array = require( '@stdlib/array-float64' );



var accumulator = incrmmeanstdev( new Float64Array( 2 ), 3 );

```



#### accumulator( \[x] )



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



```javascript

var accumulator = incrmmeanstdev( 3 );



var out = accumulator();

// returns null



// Fill the window...

out = accumulator( 2.0 ); // [2.0]

// returns [ 2.0, 0.0 ]



out = accumulator( 1.0 ); // [2.0, 1.0]

// returns [ 1.5, ~0.71 ]



out = accumulator( 3.0 ); // [2.0, 1.0, 3.0]

// returns [ 2.0, 1.0 ]



// Window begins sliding...

out = accumulator( -7.0 ); // [1.0, 3.0, -7.0]

// returns [ -1.0, ~5.29 ]



out = accumulator( -5.0 ); // [3.0, -7.0, -5.0]

// returns [ -3.0, ~5.29 ]



out = accumulator();

// returns [ -3.0, ~5.29 ]

```



## Notes



-   Input values are **not** type checked. If provided `NaN`, the accumulated values are `NaN` for **at least** `W-1` 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.

-   As `W` values are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.



## Examples



```javascript

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

var Float64Array = require( '@stdlib/array-float64' );

var ArrayBuffer = require( '@stdlib/array-buffer' );

var incrmmeanstdev = require( '@stdlib/stats-incr-mmeanstdev' );



var offset;

var acc;

var buf;

var out;

var ms;

var N;

var v;

var i;

var j;



// Define the number of accumulators:

N = 5;



// Create an array buffer for storing accumulator output:

buf = new ArrayBuffer( N*2*8 ); // 8 bytes per element



// Initialize accumulators:

acc = [];

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

    // Compute the byte offset:

    offset = i * 2 * 8; // stride=2, bytes_per_element=8



    // Create a new view for storing accumulated values:

    out = new Float64Array( buf, offset, 2 );



    // Initialize an accumulator which will write results to the view:

    acc.push( incrmmeanstdev( out, 5 ) );

}



// Simulate data and update the moving sample means and standard deviations...

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

    for ( j = 0; j < N; j++ ) {

        v = randu() * 100.0 * (j+1);

        acc[ j ]( v );

    }

}



// Print the final results:

console.log( 'Mean\tStDev' );

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

    ms = acc[ i ]();

    console.log( '%d\t%d', ms[ 0 ].toFixed( 3 ), ms[ 1 ].toFixed( 3 ) );

}

```



* * *



## See Also



-   [`@stdlib/stats-incr/meanstdev`][@stdlib/stats/incr/meanstdev]: compute an arithmetic mean and corrected sample standard deviation incrementally.

-   [`@stdlib/stats-incr/mmean`][@stdlib/stats/incr/mmean]: compute a moving arithmetic mean incrementally.

-   [`@stdlib/stats-incr/mmeanvar`][@stdlib/stats/incr/mmeanvar]: compute a moving arithmetic mean and unbiased sample variance incrementally.

-   [`@stdlib/stats-incr/mstdev`][@stdlib/stats/incr/mstdev]: compute a moving corrected sample standard deviation 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-mmeanstdev.svg

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



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

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



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

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

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

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

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

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

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

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



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



[arithmetic-mean]: https://en.wikipedia.org/wiki/Arithmetic_mean



[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation



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



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



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



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