About stdlib...
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
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!
Compute a variance-to-mean ratio (VMR) incrementally.
The unbiased sample variance is defined as
and the arithmetic mean is defined as
The variance-to-mean ratio (VMR) is thus defined as
To use in Observable,
incrvmr = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-vmr@umd/browser.js' )
To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:
var incrvmr = require( 'path/to/vendor/umd/stats-incr-vmr/index.js' )
To include the bundle in a webpage,
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-vmr@umd/browser.js"></script>
If no recognized module system is present, access bundle contents via the global scope:
<script type="text/javascript">
(function () {
window.incrvmr;
})();
</script>
Returns an accumulator function
which incrementally computes a variance-to-mean ratio.
var accumulator = incrvmr();
If the mean is already known, provide a mean
argument.
var accumulator = incrvmr( 3.0 );
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 = 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
-
Input values are not type checked. If provided
NaN
or a value which, when used in computations, results inNaN
, the accumulated value isNaN
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:
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 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 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 is also known as the index of dispersion, dispersion index, coefficient of dispersion, and relative variance.
<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-vmr@umd/browser.js"></script>
<script type="text/javascript">
(function () {
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() );
})();
</script>
</body>
</html>
@stdlib/stats-incr/mean
: compute an arithmetic mean incrementally.@stdlib/stats-incr/mvmr
: compute a moving variance-to-mean ratio (VMR) incrementally.@stdlib/stats-incr/variance
: compute an unbiased sample variance incrementally.
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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.