function incrmvmr( W, mean ) {
	var delta;
	var buf;
	var tmp;
	var M2;
	var mu;
	var d1;
	var d2;
	var N;
	var n;
	var i;
	if ( !isPositiveInteger( W ) ) {
		throw new TypeError( format( 'invalid argument. Must provide a positive integer. Value: `%s`.', W ) );
	}
	buf = new Array( W );
	n = W - 1;
	M2 = 0.0;
	i = -1;
	N = 0;
	if ( arguments.length > 1 ) {
		if ( !isNumber( mean ) ) {
			throw new TypeError( format( 'invalid argument. Must provide a number. Value: `%s`.', mean ) );
		}
		mu = mean;
		return accumulator2;
	}
	mu = 0.0;
	return accumulator1;

	/**
	* If provided a value, the accumulator function returns an updated accumulated value. If not provided a value, the accumulator function returns the current accumulated value.
	*
	* @private
	* @param {number} [x] - input value
	* @returns {(number|null)} accumulated value or null
	*/
	function accumulator1( x ) {
		var k;
		var v;
		if ( arguments.length === 0 ) {
			if ( N === 0 ) {
				return null;
			}
			if ( N === 1 ) {
				return ( isnan( M2 ) ) ? NaN : 0.0/mu;
			}
			if ( N < W ) {
				return ( M2/(N-1) ) / mu;
			}
			return ( M2/n ) / mu;
		}
		// Update the index for managing the circular buffer:
		i = (i+1) % W;

		// Case: incoming value is NaN, the sliding second moment is automatically NaN...
		if ( isnan( x ) ) {
			N = W; // explicitly set to avoid `N < W` branch
			mu = NaN;
			M2 = NaN;
		}
		// Case: initial window...
		else if ( N < W ) {
			buf[ i ] = x; // update buffer
			N += 1;
			delta = x - mu;
			mu += delta / N;
			M2 += delta * (x - mu);
			if ( N === 1 ) {
				return 0.0 / mu;
			}
			return ( M2/(N-1) ) / mu;
		}
		// Case: N = W = 1
		else if ( N === 1 ) {
			mu = x;
			M2 = 0.0;
			return M2 / mu;
		}
		// Case: outgoing value is NaN, and, thus, we need to compute the accumulated values...
		else if ( isnan( buf[ i ] ) ) {
			N = 1;
			mu = x;
			M2 = 0.0;
			for ( k = 0; k < W; k++ ) {
				if ( k !== i ) {
					v = buf[ k ];
					if ( isnan( v ) ) {
						N = W; // explicitly set to avoid `N < W` branch
						mu = NaN;
						M2 = NaN;
						break; // second moment is automatically NaN, so no need to continue
					}
					N += 1;
					delta = v - mu;
					mu += delta / N;
					M2 += delta * (v - mu);
				}
			}
		}
		// Case: neither the current second moment nor the incoming value are NaN, so we need to update the accumulated values...
		else if ( isnan( M2 ) === false ) {
			tmp = buf[ i ];
			delta = x - tmp;
			d1 = tmp - mu;
			mu += delta / W;
			d2 = x - mu;
			M2 += delta * (d1 + d2);
		}
		// Case: the current second moment is NaN, so nothing to do until the buffer no longer contains NaN values...
		buf[ i ] = x;

		return ( M2/n ) / mu;
	}

	/**
	* If provided a value, the accumulator function returns an updated accumulated value. If not provided a value, the accumulator function returns the current accumulated value.
	*
	* @private
	* @param {number} [x] - input value
	* @returns {(number|null)} accumulated value or null
	*/
	function accumulator2( x ) {
		var k;
		if ( arguments.length === 0 ) {
			if ( N === 0 ) {
				return null;
			}
			if ( N < W ) {
				return ( M2/N ) / mu;
			}
			return ( M2/W ) / mu;
		}
		// Update the index for managing the circular buffer:
		i = (i+1) % W;

		// Case: incoming value is NaN, the sliding second moment is automatically NaN...
		if ( isnan( x ) ) {
			N = W; // explicitly set to avoid `N < W` branch
			M2 = NaN;
		}
		// Case: initial window...
		else if ( N < W ) {
			buf[ i ] = x; // update buffer
			N += 1;
			delta = x - mu;
			M2 += delta * delta;
			return ( M2/N ) / mu;
		}
		// Case: outgoing value is NaN, and, thus, we need to compute the accumulated values...
		else if ( isnan( buf[ i ] ) ) {
			M2 = 0.0;
			for ( k = 0; k < W; k++ ) {
				if ( k !== i ) {
					if ( isnan( buf[ k ] ) ) {
						N = W; // explicitly set to avoid `N < W` branch
						M2 = NaN;
						break; // second moment is automatically NaN, so no need to continue
					}
					delta = buf[ k ] - mu;
					M2 += delta * delta;
				}
			}
		}
		// Case: neither the current second moment nor the incoming value are NaN, so we need to update the accumulated values...
		else if ( isnan( M2 ) === false ) {
			tmp = buf[ i ];
			M2 += ( x-tmp ) * ( x-mu + tmp-mu );
		}
		// Case: the current second moment is NaN, so nothing to do until the buffer no longer contains NaN values...
		buf[ i ] = x;

		return ( M2/W ) / mu;
	}
}
Returns an accumulator function which incrementally computes a moving variance-to-mean ratio (VMR).

## Method

-   Let \\(W\\) be a window of \\(N\\) elements over which we want to compute a variance-to-mean ratio (VMR).

-   The difference between the unbiased sample variance in a window \\(W_i\\) and the unbiased sample variance in a window \\(W_{i+1})\\) is given by

    ```tex
    \Delta s^2 = s_{i+1}^2 - s_{i}^2
    ```

-   If we multiply both sides by \\(N-1\\),

    ```tex
    (N-1)(\Delta s^2) = (N-1)s_{i+1}^2 - (N-1)s_{i}^2
    ```

-   If we substitute the definition of the unbiased sample variance having the form

    ```tex
    \begin{align*}
    s^2 &= \frac{1}{N-1} \biggl( \sum_{i=1}^{N} (x_i - \bar{x})^2 \biggr) \\
        &= \frac{1}{N-1} \biggl( \sum_{i=1}^{N} (x_i^2 - 2\bar{x}x_i + \bar{x}^2) \biggr) \\
        &= \frac{1}{N-1} \biggl( \sum_{i=1}^{N} x_i^2 - 2\bar{x} \sum_{i=1}^{N} x_i + \sum_{i=1}^{N} \bar{x}^2) \biggr) \\
        &= \frac{1}{N-1} \biggl( \sum_{i=1}^{N} x_i^2 - \frac{2N\bar{x}\sum_{i=1}^{N} x_i}{N} + N\bar{x}^2 \biggr) \\
        &= \frac{1}{N-1} \biggl( \sum_{i=1}^{N} x_i^2 - 2N\bar{x}^2 + N\bar{x}^2 \biggr) \\
        &= \frac{1}{N-1} \biggl( \sum_{i=1}^{N} x_i^2 - N\bar{x}^2 \biggr)
    \end{align*}
    ```

    we return

    ```tex
    (N-1)(\Delta s^2) = \biggl(\sum_{k=1}^N x_k^2 - N\bar{x}_{i+1}^2 \biggr) - \biggl(\sum_{k=0}^{N-1} x_k^2 - N\bar{x}_{i}^2 \biggr)
    ```

-   This can be further simplified by recognizing that subtracting the sums reduces to \\(x_N^2 - x_0^2\\); in which case,

    ```tex
    \begin{align*}
    (N-1)(\Delta s^2) &= x_N^2 - x_0^2 - N\bar{x}_{i+1}^2 + N\bar{x}_{i}^2 \\
    &= x_N^2 - x_0^2 - N(\bar{x}_{i+1}^2 - \bar{x}_{i}^2) \\
    &= x_N^2 - x_0^2 - N(\bar{x}_{i+1} - \bar{x}_{i})(\bar{x}_{i+1} + \bar{x}_{i})
    \end{align*}
    ```

-   Recognizing that the difference of means can be expressed

    ```tex
    \bar{x}_{i+1} - \bar{x}_i = \frac{1}{N} \biggl( \sum_{k=1}^N x_k - \sum_{k=0}^{N-1} x_k \biggr) = \frac{x_N - x_0}{N}
    ```

    and substituting into the equation above

    ```tex
    (N-1)(\Delta s^2) = x_N^2 - x_0^2 - (x_N - x_0)(\bar{x}_{i+1} + \bar{x}_{i})
    ```

-   Rearranging terms gives us the update equation for the unbiased sample variance

    ```tex
    \begin{align*}
    (N-1)(\Delta s^2) &= (x_N - x_0)(x_N + x_0) - (x_N - x_0)(\bar{x}_{i+1} + \bar{x}_{i})
    &= (x_N - x_0)(x_N + x_0 - \bar{x}_{i+1} - \bar{x}_{i}) \\
    &= (x_N - x_0)(x_N - \bar{x}_{i+1} + x_0 - \bar{x}_{i})
    \end{align*}
    ```

@param {PositiveInteger} W - window size
@param {number} [mean] - mean value
@throws {TypeError} first argument must be a positive integer
@throws {TypeError} second argument must be a number
@returns {Function} accumulator function

@example
var accumulator = incrmvmr( 3 );

var F = accumulator();
// returns null

F = accumulator( 2.0 );
// returns 0.0

F = accumulator( 1.0 );
// returns ~0.33

F = accumulator( 3.0 );
// returns 0.5

F = accumulator( 7.0 );
// returns ~2.55

F = accumulator();
// returns ~2.55

@example
var accumulator = incrmvmr( 3, 2.0 );