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

Compute a moving variance-to-mean ratio (VMR) incrementally.
https://github.com/stdlib-js/stats-incr-mvmr

dispersion dispersion-index fano fano-factor index-of-dispersion javascript math mathematics node node-js nodejs relative-variance sample sample-variance statistics stats stdlib unbiased variance vmr

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Compute a moving variance-to-mean ratio (VMR) incrementally.

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README 

        



  

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# incrmvmr



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



> Compute a moving [variance-to-mean ratio][variance-to-mean-ratio] (VMR) incrementally.



For a window of size `W`, the [unbiased sample variance][sample-variance] is defined as



```math

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

```



and the [arithmetic mean][arithmetic-mean] is defined as



```math

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

```



The [variance-to-mean ratio][variance-to-mean-ratio] (VMR) is thus defined as



```math

F = \frac{s^2}{\bar{x}}

```



## Installation



```bash

npm install @stdlib/stats-incr-mvmr

```



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 incrmvmr = require( '@stdlib/stats-incr-mvmr' );

```



#### incrmvmr( window\[, mean] )



Returns an accumulator `function` which incrementally computes a moving [variance-to-mean ratio][variance-to-mean-ratio]. The `window` parameter defines the number of values over which to compute the moving [variance-to-mean ratio][variance-to-mean-ratio].



```javascript

var accumulator = incrmvmr( 3 );

```



If the mean is already known, provide a `mean` argument.



```javascript

var accumulator = incrmvmr( 3, 5.0 );

```



#### accumulator( \[x] )



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



```javascript

var accumulator = incrmvmr( 3 );



var F = accumulator();

// returns null



// Fill the window...

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

// returns 0.0



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

// returns ~0.33



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

// returns 0.5



// Window begins sliding...

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

// returns ~2.55



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

// returns ~0.80



F = accumulator();

// returns ~0.80

```



## 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 **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.



-   The following table summarizes how to interpret the [variance-to-mean ratio][variance-to-mean-ratio]:



    |        VMR        |   Description   |     Example Distribution     |

    | :---------------: | :-------------: | :--------------------------: |

    |         0         |  not dispersed  |           constant           |

    | 0 < VMR < 1 | under-dispersed |           binomial           |

    |         1         |        --       |            Poisson           |

    |         >1        |  over-dispersed | geometric, negative-binomial |



    Accordingly, one can use the [variance-to-mean ratio][variance-to-mean-ratio] to assess whether observed data can be modeled as a Poisson process. When observed data is "under-dispersed", observed data may be more regular than as would be the case for a Poisson process. When observed data is "over-dispersed", observed data may contain clusters (i.e., clumped, concentrated data).



-   The [variance-to-mean ratio][variance-to-mean-ratio] is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values.



-   The [variance-to-mean ratio][variance-to-mean-ratio] is also known as the **index of dispersion**, **dispersion index**, **coefficient of dispersion**, **relative variance**, and the [**Fano factor**][fano-factor].



## Examples



```javascript

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

var incrmvmr = require( '@stdlib/stats-incr-mvmr' );



var accumulator;

var v;

var i;



// Initialize an accumulator:

accumulator = incrmvmr( 5 );



// For each simulated datum, update the moving variance-to-mean ratio...

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

    v = randu() * 100.0;

    accumulator( v );

}

console.log( accumulator() );

```



* * *



## See Also



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

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

-   [`@stdlib/stats-incr/vmr`][@stdlib/stats/incr/vmr]: compute a variance-to-mean ratio (VMR) 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-mvmr.svg

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



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

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



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

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

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

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

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

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

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

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



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



[variance-to-mean-ratio]: https://en.wikipedia.org/wiki/Index_of_dispersion



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



[sample-variance]: https://en.wikipedia.org/wiki/Variance



[fano-factor]: https://en.wikipedia.org/wiki/Fano_factor



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



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



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