On a Berry-Esseen theorem for compound Poisson processes

✍ Scribed by M.J. Goovaerts; P. Van Goethem

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 503 KB
• Volume: 4
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/0771-050x(78)90032-3

✦ Synopsis

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 byproduct the results obtained by T. H6glund [1] concerning the sum of a ftxed 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 slighdy 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].