Cumulants of random sum distributions |
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| Authors: | Naota Niki Nakagawa Shigekazu Hiieyukl Inoue |
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| Institution: | 1. Interdisciplinary Graduate School of Engineering Sciences , Kyushu University 33 , Fukuoka, 312, Japan;2. Interdisciplinary Graduate School of Engineering Sciences , Kyushu University , Kasuga-shi, Fukuoka, 816, Japan |
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| Abstract: | Consider a random variable S being the sum of a number N of independent and identically distributed random variables Xj (j = 1, 2, ...) where the number N is itself a non-negative integer-valued random variable independent of the Xj An explicit expression of the r-th cumulant of S is given in terms of the cumulants of N and Xj, Asymptotic properties of the distribution of S are also discussed. |
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| Keywords: | asymptotic expansion compound Poisson process Cornish-Fisher assumption Faà di Bruno's formula random summation |
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