Mean-preserving spread

rdf:langString Mean-preserving spread

rdf:langString 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. Ranking gambles by mean-preserving spreads is a special case of ranking gambles by second-order stochastic dominance – namely, the special case of equal means: If B is a mean-preserving spread of A, then A is second-order stochastically dominant over B; and the converse holds if A and B have equal means. If B is a mean-preserving spread of A, then B has a higher variance than A and the expected values of A and B are identical; but the converse is not in general true, because the variance is a complete ordering while ordering by mean-preserving spreads is only partial.