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In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable. In the simplest cases, the result can be either a continuous or a discrete distribution. ==Definition== Suppose that : i.e., ''N'' is a random variable whose distribution is a Poisson distribution with expected value λ, and that : are identically distributed random variables that are mutually independent and also independent of ''N''. Then the probability distribution of the sum of i.i.d. random variables conditioned on the number of these variables (): : has a well-defined distribution. In the case ''N'' = 0, then the value of ''Y'' is 0, so that then ''Y'' | ''N'' = 0 has a degenerate distribution. The compound Poisson distribution is obtained by marginalising the joint distribution of (''Y'',''N'') over ''N'', where this joint distribution is obtained by combining the conditional distribution ''Y'' | ''N'' with the marginal distribution of ''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「Compound Poisson distribution」の詳細全文を読む スポンサード リンク
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