About: Law of total cumulance

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In 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. 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

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  • In 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. 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(X1, ..., Xn) is the joint cumulant of n random variables X1, ..., Xn, and * the sum is over all partitions of the set { 1, ..., n } of indices, and * "B ∈ π;" means B runs through the whole list of "blocks" of the partition π, and * κ(Xi : 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. (en)
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  • In 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. 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 (en)
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  • Law of total cumulance (en)
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