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ITERATED PROBABILITY DISTRIBUTIONS AND

EXTREMES WITH RANDOM SAMPLE SIZE

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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.

**Source**
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