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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 Binary entropy function ： ウィキペディア英語版 Binary entropy function In information theory, the binary entropy function, denoted $\backslash operatorname\; H(p)$ or $\backslash operatorname\; H\_\backslash text(p)$, is defined as the entropy of a Bernoulli process with probability of success $p$. Mathematically, the Bernoulli trial is modelled as a random variable $X$ that can take on only two values: 0 and 1. The event $X\; =\; 1$ is considered a success and the event $X\; =\; 0$ is considered a failure. (These two events are mutually exclusive and exhaustive.) If $\backslash operatorname(X=1)\; =\; p$, then $\backslash operatorname(X=0)\; =\; 1-p$ and the entropy of $X$ (in shannons) is given by :$\backslash operatorname\; H(X)\; =\; \backslash operatorname\; H\_\backslash text(p)\; =\; -p\; \backslash log\_2\; p\; -\; (1\; -\; p)\; \backslash log\_2\; (1\; -\; p)$, where $0\; \backslash log\_2\; 0$ is taken to be 0. The logarithms in this formula are usually taken (as shown in the graph) to the base 2. See ''binary logarithm''. When $p=\backslash tfrac\; 1\; 2$, the binary entropy function attains its maximum value. This is the case of the unbiased bit, the most common unit of information entropy. $\backslash operatorname\; H(p)$ is distinguished from the entropy function $\backslash operatorname\; H(X)$ in that the former takes a single real number as a parameter whereas the latter takes a distribution or random variables as a parameter. Sometimes the binary entropy function is also written as $\backslash operatorname\; H\_2(p)$. However, it is different from and should not be confused with the Rényi entropy, which is denoted as $\backslash operatorname\; H\_2(X)$. ==Explanation== In terms of information theory, ''entropy'' is considered to be a measure of the uncertainty in a message. To put it intuitively, suppose $p=0$. At this probability, the event is certain never to occur, and so there is no uncertainty at all, leading to an entropy of 0. If $p=1$, the result is again certain, so the entropy is 0 here as well. When $p=1/2$, the uncertainty is at a maximum; if one were to place a fair bet on the outcome in this case, there is no advantage to be gained with prior knowledge of the probabilities. In this case, the entropy is maximum at a value of 1 bit. Intermediate values fall between these cases; for instance, if $p=1/4$, there is still a measure of uncertainty on the outcome, but one can still predict the outcome correctly more often than not, so the uncertainty measure, or entropy, is less than 1 full bit. 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「Binary entropy function」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.