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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 Truncated distribution ： ウィキペディア英語版 Truncated distribution In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution. Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range. For example, if the dates of birth of children in a school are examined, these would typically be subject to truncation relative to those of all children in the area given that the school accepts only children in a given age range on a specific date. There would be no information about how many children in the locality had dates of birth before or after the school's cutoff dates if only a direct approach to the school were used to obtain information. Where sampling is such as to retain knowledge of items that fall outside the required range, without recording the actual values, this is known as censoring, as opposed to the truncation here.〔Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms''. OUP. ISBN 0-19-920613-9〕 ==Definition== The following discussion is in terms of a random variable having a continuous distribution although the same ideas apply to discrete distributions. Similarly, the discussion assumes that truncation is to a semi-open interval ''y'' ∈ (''a,b''] but other possibilities can be handled straightforwardly. Suppose we have a random variable, $X$ that is distributed according to some probability density function, $f(x)$, with cumulative distribution function $F(x)$ both of which have infinite support. Suppose we wish to know the probability density of the random variable after restricting the support to be between two constants so that the support, $y\; =\; (a,b]$. That is to say, suppose we wish to know how $X$ is distributed given . : where $g(x)\; =\; f(x)$ for all There is, unfortunately, an ambiguity about the term Truncated Distribution. When one refers to a truncated distribution one could be referring to $g(x)$ where one has removed the parts from the distribution $f(x)$ but not scaled up the distribution, or one could be referring to the $Tr(x)$. In general, $g(x)$ is not a probability density function since it does not integrate to one, whereas $Tr(x)$ is a probability density function. In this article, a truncated distribution refers to $Tr(x)$ Notice that in fact is a distribution: :. Truncated distributions need not have parts removed from the top and bottom. A truncated distribution where just the bottom of the distribution has been removed is as follows: :$f(x|X>y)\; =\; \backslash frac$ where $g(x)\; =\; f(x)$ for all and $g(x)\; =\; 0$ everywhere else, and $F(x)$ is the cumulative distribution function. A truncated distribution where the top of the distribution has been removed is as follows: :$f(x|X\; \backslash leq\; y)\; =\; \backslash frac$ where $g(x)\; =\; f(x)$ for all $x\; \backslash leq\; y$ and $g(x)\; =\; 0$ everywhere else, and $F(x)$ is the cumulative distribution function. 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「Truncated distribution」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.