If I recall correctly, we can add and subtract variance if variables are independent, and have a mean of 0.
I have two distributions that are summed up: (a) one with high variance, low skewness and low kurtosis, and (b) one with lower variance, higher skewness and higher kurtosis.
I'd like to have a mathematically sound way of subtracting out portions of distribution (b). As the proportion of (a) to (b) increases, the standard deviation is increasing, while skewness and kurtosis are decreasing. Variance is the easy one, but how do I do this for skewness and kurtosis?