(Received March 30, 1994; revised February 13, 1995)
Abstract. In this paper the possible nondegenerated limit distributions for the n-fold mapping of a given probability distribution are considered. If the mapping used for the iteration procedure is a probability generating function of a positive integer-valued random variable then the results can be applied to the max-stability of distributions of random variables with random sample size.
Key words and phrases: Distribution-preserving mappings, stable distributions, extremes, random sample size.
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