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In the statistical theory of estimation, the problem of estimating the maximum of a discrete uniform distribution from sampling without replacement is known in English as the German tank problem, due to its application in World War II to the estimation of the number of German tanks. The analyses illustrate the difference between frequentist inference and Bayesian inference. Estimating the population maximum based on a ''single'' sample yields divergent results, while the estimation based on ''multiple'' samples is an instructive practical estimation question whose answer is simple but not obvious. ==Example== Suppose an intelligence officer has spotted tanks with serial numbers, 2, 6, 7, and 14, with the maximum observed serial number, . The unknown total number of tanks is called ''N''. The formula for estimating the total number of tanks suggested by the ''frequentist'' approach outlined below is : Whereas, the ''Bayesian'' analysis below yields (primarily) a probability mass function for the number of tanks : from which we can estimate the number of tanks according to : This distribution has positive skewness, related to the fact that there are at least 14 tanks. 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「German tank problem」の詳細全文を読む スポンサード リンク
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