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incrcovariance

Compute an unbiased sample covariance incrementally.

For unknown population means, the unbiased sample covariance is defined as

$$\mathop{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)$$

For known population means, the unbiased sample covariance is defined as

$$\mathop{\mathrm{cov_n}} = \frac{1}{n} \sum_{i=0}^{n-1} (x_i - \mu_x)(y_i - \mu_y)$$

Installation

npm install @stdlib/stats-incr-covariance

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 incrcovariance = require( '@stdlib/stats-incr-covariance' );

incrcovariance( [mx, my] )

Returns an accumulator function which incrementally computes an unbiased sample covariance.

var accumulator = incrcovariance();

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

var accumulator = incrcovariance( 3.0, -5.5 );

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 = incrcovariance();

var v = accumulator( 2.0, 1.0 );
// returns 0.0

v = accumulator( 1.0, -5.0 );
// returns 3.0

v = accumulator( 3.0, 3.14 );
// returns 4.07

v = accumulator();
// returns 4.07

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.

Examples

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

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

// Initialize an accumulator:
accumulator = incrcovariance();

// For each simulated datum, update the 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/mcovariance: compute a moving unbiased sample covariance incrementally.
• @stdlib/stats-incr/pcorr: compute a sample Pearson product-moment correlation coefficient.
• @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.