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incrmvariance

Compute a moving unbiased sample variance incrementally.

For a window of size W, the unbiased sample variance is defined as

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

Installation

npm install @stdlib/stats-incr-mvariance

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md 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

var incrmvariance = require( '@stdlib/stats-incr-mvariance' );

incrmvariance( window[, mean] )

Returns an accumulator function which incrementally computes a moving unbiased sample variance. The window parameter defines the number of values over which to compute the moving unbiased sample variance.

var accumulator = incrmvariance( 3 );

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

var accumulator = incrmvariance( 3, 5.0 );

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated unbiased sample variance. If not provided an input value x, the accumulator function returns the current unbiased sample variance.

var accumulator = incrmvariance( 3 );

var s2 = accumulator();
// returns null

// Fill the window...
s2 = accumulator( 2.0 ); // [2.0]
// returns 0.0

s2 = accumulator( 1.0 ); // [2.0, 1.0]
// returns 0.5

s2 = accumulator( 3.0 ); // [2.0, 1.0, 3.0]
// returns 1.0

// Window begins sliding...
s2 = accumulator( -7.0 ); // [1.0, 3.0, -7.0]
// returns 28.0

s2 = accumulator( -5.0 ); // [3.0, -7.0, -5.0]
// returns 28.0

s2 = accumulator();
// returns 28.0

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.

Examples

var randu = require( '@stdlib/random-base-randu' );
var incrmvariance = require( '@stdlib/stats-incr-mvariance' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrmvariance( 5 );

// For each simulated datum, update the moving unbiased sample variance...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );

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See Also

• @stdlib/stats-incr/mmean: compute a moving arithmetic mean incrementally.
• @stdlib/stats-incr/mstdev: compute a moving corrected sample standard deviation incrementally.
• @stdlib/stats-incr/msummary: compute a moving statistical summary incrementally.
• @stdlib/stats-incr/variance: compute an unbiased sample variance incrementally.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.