incrcovariance

Compute an unbiased sample covariance incrementally.

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

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

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() );