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incrapcorr

Compute a sample absolute Pearson product-moment correlation coefficient incrementally.

The Pearson product-moment correlation coefficient between random variables X and Y is defined as

$$\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}$$

where the numerator is the covariance and the denominator is the product of the respective standard deviations.

For a sample of size n, the sample Pearson product-moment correlation coefficient is defined as

$$r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}$$

The sample absolute Pearson product-moment correlation coefficient is thus defined as the absolute value of the sample Pearson product-moment correlation coefficient.

Usage

import incrapcorr from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-apcorr@deno/mod.js';

incrapcorr( [mx, my] )

Returns an accumulator function which incrementally computes a sample absolute Pearson product-moment correlation coefficient.

var accumulator = incrapcorr();

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

var accumulator = incrapcorr( 3.0, -5.5 );

accumulator( [x, y] )

If provided input value x and y, the accumulator function returns an updated accumulated value. If not provided input values x and y, the accumulator function returns the current accumulated value.

var accumulator = incrapcorr();

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

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

v = accumulator( 3.0, 3.14 );
// returns ~0.965

v = accumulator();
// returns ~0.965

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.
• In comparison to the sample Pearson product-moment correlation coefficient, the sample absolute Pearson product-moment correlation coefficient is useful when only concerned with the strength of the correlation and not the direction.

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import incrapcorr from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-apcorr@deno/mod.js';

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

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

// For each simulated datum, update the sample absolute correlation coefficient...
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/mapcorr: compute a moving sample absolute Pearson product-moment correlation coefficient incrementally.
• @stdlib/stats-incr/pcorr: compute a sample Pearson product-moment correlation coefficient.
• @stdlib/stats-incr/pcorr2: compute a squared sample Pearson product-moment correlation coefficient.

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Notice

This package is part of stdlib, a standard library 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.