ITERATED PROBABILITY DISTRIBUTIONS AND EXTREMES WITH RANDOM SAMPLE SIZE

B. RAUHUT

Institute of Statistics, Aachen University of Technology, D-52056 Aachen, Germany

(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.