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Negative hypergeometric distribution : ウィキペディア英語版
Negative hypergeometric distribution


In probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like Pass/Fail, Male/Female or Employed/Unemployed. As random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw. Unlike the standard hypergeometric distribution, which describes the number of successes in a fixed sample size, in the negative hypergeometric distribution, samples are drawn until R failures have been found, and the distribution describes the probability of finding k successes in such a sample. In other words, the negative hypergeometric distribution describes the likelihood of k successes in a sample with exactly R failures.
== Definition ==
There are N elements, of which K are defined as "successes" and the rest are "failures".
Elements are drawn one after the other, ''without'' replacements, until R failures are encountered. Then, the drawing stops and the number k of successes is counted. The negative hypergeometric distribution, NHG_(k) is the discrete distribution of this k.
〔(Negative hypergeometric distribution ) in Encyclopedia of Math.〕

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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