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incrmcovariance

Compute a moving unbiased sample covariance incrementally.

For unknown population means, the unbiased sample covariance for a window n of size W is defined as

$$\mathop{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=j}^{j+W-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)$$

where j specifies the index of the value at which the window begins. For example, for a trailing (i.e., non-centered) window using zero-based indexing and j greater than or equal to W, j is the n-Wth value with n being the number of values thus analyzed.

For known population means, the unbiased sample covariance for a window n of size W is defined as

$$\mathop{\mathrm{cov_n}} = \frac{1}{n} \sum_{i=j}^{j+W-1} (x_i - \mu_x)(y_i - \mu_y)$$

Installation

npm install @stdlib/stats-incr-mcovariance

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 incrmcovariance = require( '@stdlib/stats-incr-mcovariance' );

incrmcovariance( window[, mx, my] )

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

var accumulator = incrmcovariance( 3 );

If means are already known, provide mx and my arguments.

var accumulator = incrmcovariance( 3, 5.0, -3.14 );

accumulator( [x, y] )

If provided input values x and y, the accumulator function returns an updated unbiased sample covariance. If not provided input values x and y, the accumulator function returns the current unbiased sample covariance.

var accumulator = incrmcovariance( 3 );

var v = accumulator();
// returns null

// Fill the window...
v = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 0.0

v = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
// returns ~-7.49

v = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
// returns -8.35

// Window begins sliding...
v = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
// returns -29.42

v = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
// returns -24.5

v = accumulator();
// returns -24.5

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 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 (x,y) pairs 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 incrmcovariance = require( '@stdlib/stats-incr-mcovariance' );

var accumulator;
var x;
var y;
var i;

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

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

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See Also

• @stdlib/stats-incr/covariance: compute an unbiased sample covariance incrementally.
• @stdlib/stats-incr/mpcorr: compute a moving sample Pearson product-moment correlation coefficient incrementally.
• @stdlib/stats-incr/mvariance: compute a moving 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.