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incrpcorr

Compute a sample 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

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

Usage

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

incrpcorr( [mx, my] )

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

var accumulator = incrpcorr();

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

var accumulator = incrpcorr( 3.0, -5.5 );

accumulator( [x, y] )

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

var accumulator = incrpcorr();

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.

Examples

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

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

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

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

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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 © 2016-2025. The Stdlib Authors.