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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 Entropic vector ： ウィキペディア英語版 Entropic vector The entropic vector or entropic function is a concept arising in information theory. Shannon's information entropy measures and their associated identities and inequalities (both constrained and unconstrained) have received a lot of attention over the past from the time Shannon introduced his concept of Information Entropy. A lot of inequalities and identities have been found and are available in standard Information Theory texts. But recent researchers have laid focus on trying to find all possible identities and inequalities (both constrained and unconstrained) on such entropies and characterize them. Entropic vector lays down the basic framework for such a study. ==Definition== Let $X\_1,\; X\_2,\backslash dots,X\_n$ be random variables, with $n\; \backslash in\; N$ A vector ''h'' in $R^$ is an entropic vector of order $n$ if and only if there exists a tuple $\backslash overrightarrow=X\_1,X\_2,\backslash ldots,X\_n$ with associated vector $h\_\}(I)=H(X\_I)=H(X\_,X\_,\backslash dots,X\_)$ where $I=\backslash$ y $h=h\_\{\backslash overrightarrow\{x\}\}$. The set of all entropic vectors of order $n$ is denoted by $\backslash Gamma\_n^$ * All the properties of entropic functions can be transposed to entropic vectors: $H\; :P\_n\; \backslash rightarrow\; R^+$ is continuous Given a deterministic random variable $x$, we have $H(x)=0$ Given $\backslash alpha\; \backslash in\; R^+$, there exists a random variable $x$ such that $H(x)=\backslash alpha$ Given $P$ a probability distribution on $()$, we have $H(P)\backslash leq\; \backslash log\_2\; n$ 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「Entropic vector」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.