incrpcorrdist

Compute a sample Pearson product-moment correlation distance incrementally.

The sample Pearson product-moment correlation distance is defined as

d Subscript x comma y Baseline equals 1 minus r Subscript x comma y Baseline equals 1 minus StartFraction normal c normal o normal v Subscript normal n Baseline left-parenthesis normal x comma normal y right-parenthesis Over sigma Subscript x Baseline sigma Subscript y Baseline EndFraction

where r is the sample Pearson product-moment correlation coefficient, cov(x,y) is the sample covariance, and σ corresponds to the sample standard deviation. As r resides on the interval [-1,1], d resides on the interval [0,2].

Usage

var incrpcorrdist = require( '@stdlib/stats/incr/pcorrdist' );

incrpcorrdist( [mx, my] )

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

var accumulator = incrpcorrdist();

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

var accumulator = incrpcorrdist( 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 = incrpcorrdist();

var d = accumulator( 2.0, 1.0 );
// returns 1.0

d = accumulator( 1.0, -5.0 );
// returns 0.0

d = accumulator( 3.0, 3.14 );
// returns ~0.035

d = accumulator();
// returns ~0.035

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 incrpcorrdist = require( '@stdlib/stats/incr/pcorrdist' );

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

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

// For each simulated datum, update the sample correlation distance...
for ( i = 0; i < 100; i++ ) {
    x = randu() * 100.0;
    y = randu() * 100.0;
    accumulator( x, y );
}
console.log( accumulator() );