incrcovariance

Compute an unbiased sample covariance incrementally.

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

normal c normal o normal v Subscript normal n Baseline equals StartFraction 1 Over n minus 1 EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis x Subscript i Baseline minus x overbar Subscript n Baseline right-parenthesis left-parenthesis y Subscript i Baseline minus y overbar Subscript n Baseline right-parenthesis

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

normal c normal o normal v Subscript normal n Baseline equals StartFraction 1 Over n EndFraction sigma-summation Underscript i equals 0 Overscript n minus 1 Endscripts left-parenthesis x Subscript i Baseline minus mu Subscript x Baseline right-parenthesis left-parenthesis y Subscript i Baseline minus mu Subscript y Baseline right-parenthesis

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() );