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About: Mean-preserving spread     Goto   Sponge   NotDistinct   Permalink

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In probability and statistics, a mean-preserving spread (MPS) is a change from one probability distribution A to another probability distribution B, where B is formed by spreading out one or more portions of A's probability density function or probability mass function while leaving the mean (the expected value) unchanged. As such, the concept of mean-preserving spreads provides a stochastic ordering of equal-mean gambles (probability distributions) according to their degree of risk; this ordering is partial, meaning that of two equal-mean gambles, it is not necessarily true that either is a mean-preserving spread of the other. Distribution A is said to be a mean-preserving contraction of B if B is a mean-preserving spread of A.