Stability of extremes with random sample size

A non-degenerate distribution function F is called maximum stable with random sample size if there exist positive integer random variables Nn, n = 1, 2, ···, with P(Nn = 1) less than 1 and tending to 1 as n → ∞ and such that F and the distribution function of the maximum value of Nn independent obse...

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Bibliographic Details
Published in:Journal of applied probability 1989-12, Vol.26 (4), p.734-743
Main Author: Voorn, W. J.
Format: Article
Language:English
Subjects:
Coefficients
Distribution functions
Distribution theory
Exact sciences and technology
Integers
Mathematical theorems
Mathematics
Power series
Power series coefficients
Probability and statistics
Probability distributions
Probability theory and stochastic processes
Random variables
Real numbers
Research Papers
Sample size
Sciences and techniques of general use
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Summary:A non-degenerate distribution function F is called maximum stable with random sample size if there exist positive integer random variables Nn, n = 1, 2, ···, with P(Nn = 1) less than 1 and tending to 1 as n → ∞ and such that F and the distribution function of the maximum value of Nn independent observations from F (and independent of Nn ) are of the same type for every index n. By proving the converse of an earlier result of the author, it is shown that the set of all maximum stable distribution functions with random sample size consists of all distribution functions F satisfying where c 2, c 3, · ·· are arbitrary non-negative constants with 0 < c2 + c3 + · ··
ISSN:0021-9002
1475-6072
DOI:10.2307/3214378