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An alternative to a moment as part of a summary of the form of a distribution. If the moment-generating function of a distribution exists, then its natural logarithm exists and is called the cumulant-generating function (cgf). The coefficient of tr/r! in the Taylor expansion of the cgf is called the rth cumulant and is denoted by κr (where κ is kappa). The cumulants can be expressed in terms of the central moments, and vice versa. In particular, denoting the mean by μ and the central moments by μ2, μ3,…,. For an example of the application of cumulants, see Cornish–Fisher expansion.

Subjects: Probability and Statistics.

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