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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mean-preserving spread ： ウィキペディア英語版 Mean-preserving spread In probability and statistics, a mean-preserving spread (MPS)〔Rothschild, Michael, and Stiglitz, Joseph, "Increasing risk I: A definition," ''Journal of Economic Theory'', 1970, 225–243.〕 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. 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 value 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. ==Example== This example from 〔Landsberger, M., and Meilijson, I., "Mean-preserving portfolio dominance," ''Review of Economic Studies'' 60, April 1993, 479–485.〕 shows that to have a mean-preserving spread does not require that all or most of the probability mass move away from the mean. Let A have equal probabilities $1/100$ on each outcome $x\_$ , with $x\_=198$ for $i=1,\backslash dots,\; 50$ and $x\_=202$ for $i=51,\backslash dots,100$; and let B have equal probabilities $1/100$ on each outcome $x\_$, with $x\_=100$, $x\_=200$ for $i=2,\backslash dots,99$, and $x\_=300$. Here B has been constructed from A by moving one chunk of 1% probability from 198 to 100 and moving 49 probability chunks from 198 to 200, and then moving one probability chunk from 202 to 300 and moving 49 probability chunks from 202 to 200. This sequence of two mean-preserving spreads is itself a mean-preserving spread, despite the fact that 98% of the probability mass has moved to the mean (200). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Mean-preserving spread」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.