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(詳細はprobability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance. It has applications in the analysis of time series. It was introduced by David Brillinger.〔David Brillinger, "The calculation of cumulants via conditioning", ''Annals of the Institute of Statistical Mathematics'', Vol. 21 (1969), pp. 215–218.〕 It is most transparent when stated in its most general form, for ''joint'' cumulants, rather than for cumulants of a specified order for just one random variable. In general, we have : where * κ(''X''1, ..., ''X''''n'') is the joint cumulant of ''n'' random variables ''X''1, ..., ''X''''n'', and * the sum is over all partitions of the set of indices, and * "''B'' ∈ π" means ''B'' runs through the whole list of "blocks" of the partition π, and * κ(''X''''i'' : ''i'' ∈ ''B'' | ''Y'') is a conditional cumulant given the value of the random variable ''Y''. It is therefore a random variable in its own right—a function of the random variable ''Y''. ==Examples== 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「Law of total cumulance」の詳細全文を読む スポンサード リンク
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