Cokurtosis
In probability theory and statistics, cokurtosis is a measure of how much two random variables change together. Cokurtosis is the fourth standardized cross central moment. If two random variables exhibit a high level of cokurtosis they will tend to undergo extreme positive and negative deviations at the same time. Definition For two random variables X and Y there are three non-trivial cokurtosis statistics and where E[X] is the expected value of X, also known as the mean of X, and is the standard deviation of X. Properties Kurtosis is a special case of the cokurtosis when the two random variables are identical: For two random variables, X and Y, the kurtosis of the sum, X + Y, is where is the kurtosis of X and is the standard deviation of X. It follows that the sum of two random variables can have kurtosis different from 3 () even if both random variables have kurtosis of 3 in isolation ( and ). The cokurtosis between variables X and Y does not depend on the scale on which the variables are expressed. If we are analyzing the relationship between X and Y, the cokurtosis between X and Y will be the same