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• W1970502407 abstract "The well-known Berry-Esseen theorem concerning the rate of convergence to a stable law for a sum of independent identically distributed (i.i.d.) random variables is adapted to the case of a compound Poisson process, considered in the collective risk theory. As a consequence the rate of convergence of the Edgeworth expansion to the compound Poisson distribution is examined for all positive values of the time variable, in both cases where the moments of the claim distribution converge or diverge. As a by product the results obtained by T. Höglund [1] concerning the sum of a fixed number (n) of i.i.d. random variables are presented in an alternative manner. His theorems concerning the limiting behaviour for n → ∞ can be transformed slightly in order to make them hold for all n. It is explained how the result on the estimation of the rate of convergence in a limit theorem with a stable law fits with the results obtained by K.I. Satyabaldina [2]." @default.
• W1970502407 created "2016-06-24" @default.
• W1970502407 creator A5025060418 @default.
• W1970502407 creator A5044522512 @default.
• W1970502407 date "1978-06-01" @default.
• W1970502407 modified "2023-09-23" @default.
• W1970502407 title "On a Berry-Esseen theorem for compound Poisson processes" @default.
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• W1970502407 doi "https://doi.org/10.1016/0771-050x(78)90032-3" @default.
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