Eaton's inequality is a result in probability theory that deals with the relationship between the expectations of certain types of random variables, particularly focused on sub-exponential distributions. It is useful in the context of assessing the tail behavior of distributions. Formally, Eaton's inequality provides a way to compare the expectations of a sub-exponential random variable \(X\) and a positive continuous random variable \(Y\) with respect to their expectations given that their values are non-negative.
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