Informatics and Applications
2014, Volume 8, Issue 3, pp 3-11
ON CONDITIONS OF CONVERGENCE OF THE DISTRIBUTIONS OF EXTREMAL ORDER STATISTICS TO THE WEIBULL DISTRIBUTION
Abstract
Some product representations are obtained
for random variables with the Weibull distribution by stable
random variables. These results are used to describe the conditions
providing convergence of the distributions of linearly transformed
minimum order statistics in samples with random sizes to the Weibull
distribution. The presented results broaden traditional conceptions
concerning conditions of convergence of extremal order statistics to
the Weibull distribution and give additional theoretical explanation
for high adequacy of the Weibull distribution in lifetime data analysis,
in particular, in reliability theory.
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[+] About this article
Title
ON CONDITIONS OF CONVERGENCE OF THE DISTRIBUTIONS OF EXTREMAL ORDER STATISTICS TO THE WEIBULL DISTRIBUTION
Journal
Informatics and Applications
2014, Volume 8, Issue 3, pp 3-11
Cover Date
2014-03-31
DOI
10.14357/19922264140301
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Weibull distribution; exponential distribution; Rayleigh distribution; strictly stable distribution; sample with random size
Authors
V.Yu.Korolev , and I.A.Sokolov
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics,
M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, Moscow 119991, GSP-1, Russian
Federation
Institute of Informatics Problems, Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian
Federation
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