incrmpcorrdist

Compute a moving sample Pearson product-moment correlation distance incrementally.

The sample Pearson product-moment correlation distance is defined as

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 incrmpcorrdist = require( '@stdlib/stats/incr/mpcorrdist' );

incrmpcorrdist( window[, mx, my] )

Returns an accumulator function which incrementally computes a moving sample Pearson product-moment correlation distance. The window parameter defines the number of values over which to compute the moving sample Pearson product-moment correlation distance.

var accumulator = incrmpcorrdist( 3 );

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

var accumulator = incrmpcorrdist( 3, 5.0, -3.14 );

accumulator( [x, y] )

If provided input values x and y, the accumulator function returns an updated sample Pearson product-moment correlation distance. If not provided input values x and y, the accumulator function returns the current sample Pearson product-moment correlation distance.

var accumulator = incrmpcorrdist( 3 );

var r = accumulator();
// returns null

// Fill the window...
r = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 1.0

r = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
// returns ~2.0

r = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
// returns ~1.925

// Window begins sliding...
r = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
// returns ~1.863

r = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
// returns ~1.803

r = accumulator();
// returns ~1.803

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 at least W-1 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.
As W (x,y) pairs are needed to fill the window buffer, the first W-1 returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.
Due to limitations inherent in representing numeric values using floating-point format (i.e., the inability to represent numeric values with infinite precision), the sample correlation distance between perfectly correlated random variables may not be 0 or 2. In fact, the sample correlation distance is not guaranteed to be strictly on the interval [0,2]. Any computed distance should, however, be within floating-point roundoff error.

Examples

var randu = require( '@stdlib/random/base/randu' );
var incrmpcorrdist = require( '@stdlib/stats/incr/mpcorrdist' );

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

// Initialize an accumulator:
accumulator = incrmpcorrdist( 5 );

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