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

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

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

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

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README 

        



  

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# incrvmr



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



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



The [unbiased sample variance][sample-variance] is defined as



```math

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

```



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



```math

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

```



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



```math

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

```



## Installation



```bash

npm install @stdlib/stats-incr-vmr

```



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 incrvmr = require( '@stdlib/stats-incr-vmr' );

```



#### incrvmr( \[mean] )



Returns an accumulator `function` which incrementally computes a [variance-to-mean ratio][variance-to-mean-ratio].



```javascript

var accumulator = incrvmr();

```



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



```javascript

var accumulator = incrvmr( 3.0 );

```



#### 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 = incrvmr();



var D = accumulator( 2.0 );

// returns 0.0



D = accumulator( 1.0 ); // => s^2 = ((2-1.5)^2+(1-1.5)^2) / (2-1)

// returns ~0.33



D = accumulator( 3.0 ); // => s^2 = ((2-2)^2+(1-2)^2+(3-2)^2) / (3-1)

// returns 0.5



D = accumulator();

// returns 0.5

```



## 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.



-   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**, and **relative variance**.



## Examples



```javascript

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

var incrvmr = require( '@stdlib/stats-incr-vmr' );



var accumulator;

var v;

var i;



// Initialize an accumulator:

accumulator = incrvmr();



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

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

    v = randu() * 100.0;

    accumulator( v );

}

console.log( accumulator() );

```



* * *



## See Also



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

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

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



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

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



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

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

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

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

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

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

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

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



[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-incr-vmr/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



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



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



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