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 Subscript upper X comma upper Y Baseline equals StartFraction c o v left-parenthesis upper X comma upper Y right-parenthesis Over sigma Subscript upper X Baseline sigma Subscript upper Y Baseline EndFraction

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 equals StartFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis x Subscript i Baseline minus x overbar right-parenthesis left-parenthesis y Subscript i Baseline minus y overbar right-parenthesis Over StartRoot sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis x Subscript i Baseline minus x overbar right-parenthesis squared EndRoot StartRoot sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis y Subscript i Baseline minus y overbar right-parenthesis squared EndRoot EndFraction

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

Usage

var incrapcorr = require( '@stdlib/stats/incr/apcorr' );

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

var randu = require( '@stdlib/random/base/randu' );
var incrapcorr = require( '@stdlib/stats/incr/apcorr' );

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() );