incrmvmr
Compute a moving variancetomean ratio (VMR) incrementally.
For a window of size W
, the unbiased sample variance is defined as
and the arithmetic mean is defined as
The variancetomean ratio (VMR) is thus defined as
Installation
npm install @stdlib/statsincrmvmr
Usage
var incrmvmr = require( '@stdlib/statsincrmvmr' );
incrmvmr( window[, mean] )
Returns an accumulator function
which incrementally computes a moving variancetomean ratio. The window
parameter defines the number of values over which to compute the moving variancetomean ratio.
var accumulator = incrmvmr( 3 );
If the mean is already known, provide a mean
argument.
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.
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 inNaN
, the accumulated value isNaN
for at leastW1
future invocations. If nonnumeric 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 firstW1
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 variancetomean ratio:
VMR Description Example Distribution 0 not dispersed constant 0 < VMR < 1 underdispersed binomial 1  Poisson >1 overdispersed geometric, negativebinomial Accordingly, one can use the variancetomean ratio to assess whether observed data can be modeled as a Poisson process. When observed data is "underdispersed", observed data may be more regular than as would be the case for a Poisson process. When observed data is "overdispersed", observed data may contain clusters (i.e., clumped, concentrated data).

The variancetomean ratio is typically computed on nonnegative values. The measure may lack meaning for data which can assume both positive and negative values.

The variancetomean ratio is also known as the index of dispersion, dispersion index, coefficient of dispersion, relative variance, and the Fano factor.
Examples
var randu = require( '@stdlib/randombaserandu' );
var incrmvmr = require( '@stdlib/statsincrmvmr' );
var accumulator;
var v;
var i;
// Initialize an accumulator:
accumulator = incrmvmr( 5 );
// For each simulated datum, update the moving variancetomean ratio...
for ( i = 0; i < 100; i++ ) {
v = randu() * 100.0;
accumulator( v );
}
console.log( accumulator() );
See Also

@stdlib/stats/incr/mmean
: compute a moving arithmetic mean incrementally. 
@stdlib/stats/incr/mvariance
: compute a moving unbiased sample variance incrementally. 
@stdlib/stats/incr/vmr
: compute a variancetomean ratio (VMR) incrementally.
Notice
This package is part of 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, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 20162022. The Stdlib Authors.