How to Distinguish True Dependence from Varying

Abstract

A usual statistical criterion for the quantities X and Y to be independent is that the corresponding distribution function F(x,y) is equal to the product of the corresponding marginal distribution functions. If this equality is violated, this is usually taken to mean that X and Y are dependent. In practice, however, the inequality may be caused by the fact that we have a mixture of several populations, in each of which X and Y are independent. In this paper, we show how we can distinguish true dependence from such varying independence. This can also lead to new measures to degree of independence and of varying independence.