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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 Hypergeometric distribution ： ウィキペディア英語版 Hypergeometric distribution \, | pdf = $$ | cdf = $1-\}\backslash over\; \}\; \backslash ,\_3F\_2\backslash !\backslash !\backslash left(k+1-K,\backslash \; k+1-n\; \backslash \backslash \; k+2,\backslash \; N+k+2-K-n\backslash end;1\backslash right)$ | mean = $n$ | median = | mode = $\backslash left\; \backslash lfloor\; \backslash frac\; \backslash right\; \backslash rfloor$ | variance = $n$ | skewness = $\backslash frac(N-2n)\}(N-2)\}$ | kurtosis = $\backslash left.\backslash frac\backslash cdot\backslash right.$ | entropy = | mgf = $\backslash frac$ In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of $k$ successes in $n$ draws, ''without'' replacement, from a finite population of size $N$ that contains exactly $K$ successes, wherein each draw is either a success or a failure. In contrast, the binomial distribution describes the probability of $k$ successes in $n$ draws ''with'' replacement. In statistics, the hypergeometric test uses the hypergeometric distribution to calculate the statistical significance of having drawn a specific $k$ successes (out of $n$ total draws) from the aforementioned population. The test is often used to identify which sub-populations are over- or under-represented in a sample. This test has a wide range of applications. For example, a marketing group could use the test to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups (e.g., women, people under 30). ==Definition== The following conditions characterize the hypergeometric distribution: * The result of each draw (the elements of the population being sampled) can be classified into one of two mutually exclusive categories (e.g. Pass/Fail or Female/Male or Employed/Unemployed). * The probability of a success changes on each draw, as each draw decreases the population (''sampling without replacement'' from a finite population). A random variable $X$ follows the hypergeometric distribution if its probability mass function (pmf) is given by :$P(X\; =\; k)\; =\; \backslash frac\; \backslash binom\}\}$, where *$N$ is the population size, *$K$ is the number of success states in the population, *$n$ is the number of draws, *$k$ is the number of observed successes, *$\backslash textstyle$ is a binomial coefficient. The pmf is positive when $\backslash max(0,\; n+K-N)\; \backslash leq\; k\; \backslash leq\; \backslash min(K,n)$. The pmf satisfies the recurrence relation : $(k\; +\; 1)\; (N\; -\; K\; -\; (n\; -\; k\; -\; 1))\; P(X\; =\; k\; +\; 1)\; =\; (K\; -\; k)\; (n\; -\; k)\; P(X\; =\; k)$ with : $P(X\; =\; 0)\; =\; \backslash frac\}\}$. 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「Hypergeometric 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.