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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 Schrödinger method ： ウィキペディア英語版 Schrödinger method In combinatorial mathematics and probability theory, the Schrödinger method, named after the Austrian physicist Erwin Schrödinger, is used to solve some problems of distribution and occupancy. Suppose :$X\_1,\backslash dots,X\_n\; \backslash ,$ are independent random variables that are uniformly distributed on the interval (). Let :$X\_,\backslash dots,X\_\; \backslash ,$ be the corresponding order statistics, i.e., the result of sorting these ''n'' random variables into increasing order. We seek the probability of some event ''A'' defined in terms of these order statistics. For example, we might seek the probability that in a certain seven-day period there were at most two days in on which only one phone call was received, given that the number of phone calls during that time was 20. This assumes uniform distribution of arrival times. The Schrödinger method begins by assigning a Poisson distribution with expected value ''λt'' to the number of observations in the interval (), the number of observations in non-overlapping subintervals being independent (see Poisson process). The number ''N'' of observations is Poisson-distributed with expected value ''λ''. Then we rely on the fact that the conditional probability :$P(A\backslash mid\; N=n)\; \backslash ,$ does not depend on ''λ'' (in the language of statisticians, ''N'' is a sufficient statistic for this parametrized family of probability distributions for the order statistics). We proceed as follows: :$P\_\backslash lambda(A)=\backslash sum\_^\backslash infty\; P(A\backslash mid\; N=n)P(N=n)=\backslash sum\_^\backslash infty\; P(A\backslash mid\; N=n),$ so that :$e^\backslash ,P\_\backslash lambda(A)=\backslash sum\_^\backslash infty\; P(A\backslash mid\; N=n).$ Now the lack of dependence of ''P''(''A'' | ''N'' = ''n'') upon ''λ'' entails that the last sum displayed above is a power series in ''λ'' and ''P''(''A'' | ''N'' = ''n'') is the value of its ''n''th derivative at ''λ'' = 0, i.e., : ■ウィキペディアで「Schrödinger method」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.