function incrpcorr( meanx, meany ) {
	var M2x;
	var M2y;
	var dy1;
	var dy2;
	var dy;
	var dx;
	var mx;
	var my;
	var sx;
	var sy;
	var C;
	var N;

	M2x = 0.0;
	M2y = 0.0;
	C = 0.0;
	N = 0;
	if ( arguments.length ) {
		if ( !isNumber( meanx ) ) {
			throw new TypeError( format( 'invalid argument. First argument must be a number. Value: `%s`.', meanx ) );
		}
		if ( !isNumber( meany ) ) {
			throw new TypeError( format( 'invalid argument. Second argument must be a number. Value: `%s`.', meany ) );
		}
		mx = meanx;
		my = meany;
		return accumulator2;
	}
	mx = 0.0;
	my = 0.0;
	return accumulator1;

	/**
	* If provided input values, the accumulator function returns an updated sample correlation coefficient. If not provided input values, the accumulator function returns the current sample correlation coefficient.
	*
	* @private
	* @param {number} [x] - new value
	* @param {number} [y] - new value
	* @returns {(number|null)} sample correlation coefficient or null
	*/
	function accumulator1( x, y ) {
		var n;
		if ( arguments.length === 0 ) {
			if ( N === 0 ) {
				return null;
			}
			if ( N === 1 ) {
				return ( isnan( M2x ) || isnan( M2y ) ) ? NaN : 0.0;
			}
			return ( C/(N-1) ) / ( sx*sy );
		}
		N += 1;

		dx = x - mx;
		mx += dx / N;
		M2x += dx * ( x-mx );

		dy1 = y - my;
		my += dy1 / N;
		dy2 = y - my;
		M2y += dy2 * dy1;

		C += dx * dy2;
		if ( N < 2 ) {
			return ( isnan( M2x ) || isnan( M2y ) ) ? NaN : 0.0;
		}
		n = N - 1;
		sx = sqrt( M2x/n );
		sy = sqrt( M2y/n );
		return ( C/n ) / ( sx*sy ); // Note: why all the dividing by `N`? To avoid overflow.
	}

	/**
	* If provided input values, the accumulator function returns an updated sample correlation coefficient. If not provided input values, the accumulator function returns the current sample correlation coefficient.
	*
	* @private
	* @param {number} [x] - new value
	* @param {number} [y] - new value
	* @returns {(number|null)} sample correlation coefficient or null
	*/
	function accumulator2( x, y ) {
		if ( arguments.length === 0 ) {
			if ( N === 0 ) {
				return null;
			}
			return ( C/N ) / ( sx*sy );
		}
		N += 1;

		dx = x - mx;
		M2x += dx * dx;

		dy = y - my;
		M2y += dy * dy;

		C += dx * dy;
		sx = sqrt( M2x/N );
		sy = sqrt( M2y/N );
		return ( C/N ) / ( sx*sy ); // Note: why all the dividing by `N`? To avoid overflow.
	}
}
Returns an accumulator function which incrementally computes a sample Pearson product-moment correlation coefficient.

## Method

-   We begin by defining the co-moment \\(C_n\\)

    ```tex
    C_n = \sum_{i=1}^{n} ( x_i - \bar{x}_n ) ( y_i - \bar{y}_n )
    ```

    where \\(\bar{x}_n\\) and \\(\bar{y}_n\\) are the sample means for \\(x\\) and \\(y\\), respectively.

-   Based on Welford's method, we know the update formulas for the sample means are given by

    ```tex
    \bar{x}_n = \bar{x}_{n-1} + \frac{x_n - \bar{x}_{n-1}}{n}
    ```

    and

    ```tex
    \bar{y}_n = \bar{y}_{n-1} + \frac{y_n - \bar{y}_{n-1}}{n}
    ```

-   Substituting into the equation for \\(C_n\\) and rearranging terms

    ```tex
    C_n = C_{n-1} + (x_n - \bar{x}_n) (y_n - \bar{y}_{n-1})
    ```

    where the apparent asymmetry arises from

    ```tex
    x_n - \bar{x}_n = \frac{n-1}{n} (x_n - \bar{x}_{n-1})
    ```

    and, hence, the update term can be equivalently expressed

    ```tex
    \frac{n-1}{n} (x_n - \bar{x}_{n-1}) (y_n - \bar{y}_{n-1})
    ```

-   The covariance can be defined

    ```tex
    \begin{align*}
    \operatorname{cov}_n(x,y) &= \frac{C_n}{n} \\
    &= \frac{C_{n-1} + (x_n - \bar{x}_n) (y_n - \bar{y}_{n-1})}{n} \\
    &= \frac{(n-1)\operatorname{cov}_{n-1}(x,y) + (x_n - \bar{x}_n) (y_n - \bar{y}_{n-1})}{n}
    \end{align*}
    ```

-   Applying Bessel's correction, we arrive at an update formula for calculating an unbiased sample covariance

    ```tex
    \begin{align*}
    \operatorname{cov}_n(x,y) &= \frac{n}{n-1}\cdot\frac{(n-1)\operatorname{cov}_{n-1}(x,y) + (x_n - \bar{x}_n) (y_n - \bar{y}_{n-1})}{n} \\
    &= \operatorname{cov}_{n-1}(x,y) + \frac{(x_n - \bar{x}_n) (y_n - \bar{y}_{n-1})}{n-1} \\
    &= \frac{C_{n-1} + (x_n - \bar{x}_n) (y_n - \bar{y}_{n-1})}{n-1}
    &= \frac{C_{n-1} + (x_n - \bar{x}_{n-1}) (y_n - \bar{y}_n)}{n-1}
    \end{align*}
    ```

-   To calculate the corrected sample standard deviation, we can use Welford's method, which can be derived as follows. We can express the variance as

    ```tex
    \begin{align*}
    S_n &= n \sigma_n^2 \\
        &= \sum_{i=1}^{n} (x_i - \mu_n)^2 \\
        &= \biggl(\sum_{i=1}^{n} x_i^2 \biggr) - n\mu_n^2
    \end{align*}
    ```

    Accordingly,

    ```tex
    \begin{align*}
    S_n - S_{n-1} &= \sum_{i=1}^{n} x_i^2 - n\mu_n^2 - \sum_{i=1}^{n-1} x_i^2 + (n-1)\mu_{n-1}^2 \\
                  &= x_n^2 - n\mu_n^2 + (n-1)\mu_{n-1}^2 \\
                  &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1}^2 - \mu_n^2) \\
                  &= x_n^2 - \mu_{n-1}^2 + n(\mu_{n-1} - \mu_n)(\mu_{n-1} + \mu_n) \\
                  &= x_n^2 - \mu_{n-1}^2 + (\mu_{n-1} - x_n)(\mu_{n-1} + \mu_n) \\
                  &= x_n^2 - \mu_{n-1}^2 + \mu_{n-1}^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
                  &= x_n^2 - x_n\mu_n - x_n\mu_{n-1} + \mu_n\mu_{n-1} \\
                  &= (x_n - \mu_{n-1})(x_n - \mu_n) \\
                  &= S_{n-1} + (x_n - \mu_{n-1})(x_n - \mu_n)
    \end{align*}
    ```

    where we use the identity

    ```tex
    x_n - \mu_{n-1} = n (\mu_n - \mu_{n-1})
    ```

-   To compute the corrected sample standard deviation, we apply Bessel's correction and take the square root.

-   The sample Pearson product-moment correlation coefficient can thus be calculated as

    ```tex
    r = \frac{\operatorname{cov}_n(x,y)}{\sigma_x \sigma_y}
    ```

    where \\(\sigma_x\\) and \\(\sigma_y\\) are the corrected sample standard deviations for \\(x\\) and \\(y\\), respectively.

@param {number} [meanx] - mean value
@param {number} [meany] - mean value
@throws {TypeError} first argument must be a number
@throws {TypeError} second argument must be a number
@returns {Function} accumulator function

@example
var accumulator = incrpcorr();

var r = accumulator();
// returns null

r = accumulator( 2.0, 1.0 );
// returns 0.0

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

r = accumulator();
// returns ~-1.0

@example
var accumulator = incrpcorr( 2.0, -3.0 );