Compute a moving sample Pearson product-moment correlation coefficient incrementally.
The Pearson product-moment correlation coefficient between random variables X and Y is defined as
where the numerator is the covariance and the denominator is the product of the respective standard deviations.
For a sample of size W, the sample Pearson product-moment correlation coefficient is defined as
var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
Returns an accumulator function which incrementally computes a moving sample Pearson product-moment correlation coefficient. The window parameter defines the number of values over which to compute the moving sample Pearson product-moment correlation coefficient.
var accumulator = incrmpcorr( 3 );
If means are already known, provide mx and my arguments.
var accumulator = incrmpcorr( 3, 5.0, -3.14 );
If provided input values x and y, the accumulator function returns an updated sample Pearson product-moment correlation coefficient. If not provided input values x and y, the accumulator function returns the current sample Pearson product-moment correlation coefficient.
var accumulator = incrmpcorr( 3 );
var r = accumulator();
// returns null
// Fill the window...
r = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 0.0
r = accumulator( -5.0, 3.14 ); // [(2.0, 1.0), (-5.0, 3.14)]
// returns ~-1.0
r = accumulator( 3.0, -1.0 ); // [(2.0, 1.0), (-5.0, 3.14), (3.0, -1.0)]
// returns ~-0.925
// Window begins sliding...
r = accumulator( 5.0, -9.5 ); // [(-5.0, 3.14), (3.0, -1.0), (5.0, -9.5)]
// returns ~-0.863
r = accumulator( -5.0, 1.5 ); // [(3.0, -1.0), (5.0, -9.5), (-5.0, 1.5)]
// returns ~-0.803
r = accumulator();
// returns ~-0.803
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.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.var randu = require( '@stdlib/random/base/randu' );
var incrmpcorr = require( '@stdlib/stats/incr/mpcorr' );
var accumulator;
var x;
var y;
var i;
// Initialize an accumulator:
accumulator = incrmpcorr( 5 );
// For each simulated datum, update the moving sample correlation coefficient...
for ( i = 0; i < 100; i++ ) {
x = randu() * 100.0;
y = randu() * 100.0;
accumulator( x, y );
}
console.log( accumulator() );