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In probability and statistics, a compound probability distribution is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with the parameters of that distribution being assumed to be themselves random variables. The compound distribution is the result of marginalizing over the intermediate random variables that represent the parameters of the initial distribution. An important type of compound distribution occurs when the parameter being marginalized over represents the number of random variables in a summation of random variables. ==Definition== A compound probability distribution is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution with an unknown parameter ''θ'' or parameter vector θ that is distributed according to some other distribution ''G'' with hyperparameter ''α'', and then determining the distribution that results from marginalizing over ''G'' (i.e. integrating the unknown parameter(s) out). The resulting distribution ''H'' is said to be the distribution that results from compounding ''F'' with ''G''. Expressed mathematically for a scalar data point with scalar parameter and hyperparameter: : The same formula applies if some or all of the variables are vectors. Here is the case for a vector data point with vector parameters and hyperparameters: : A compound distribution resembles in many ways the original distribution that generated it, but typically has greater variance, and often heavy tails as well. The support of is the same as the support of the , and often the shape is broadly similar as well. The parameters of include the parameters of and any parameters of that are not marginalized out. 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 probability distribution」の詳細全文を読む スポンサード リンク
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