Derivations of the compound Poisson distribution and process

Y. H. Wang and Shuixin Ji

Statistics & Probability Letters, 1993, vol. 18, issue 1, 1-7

Abstract: For a sequence of independent integer-valued random variables {Xni}, we give a direct proof of the convergence of the distribution of Sn=Xn1+...+Xnn to a compound Poisson distribution with discrete compounding distribution. In our proof, we trace the change in the asymptotical behavior of Sn from the Poisson to the compound Poisson distribution as the range of {Xni} is expanded from {0, 1} to general subsets of the integers. The corresponding results for the axiomatic derivations of the compound Poisson processes are also obtained.

Keywords: Sum; of; random; variables; limit; distribution; Poisson; compound; Poisson; stochastic; process; characterization (search for similar items in EconPapers)
Date: 1993
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