Some asymptotic results on extremes of incomplete samples

Let X 1 , X 2 , ⋯ be a sequence of independent and identically distributed random variables and M n  =  max { X 1 , X 2 , ⋯ , X n }. Suppose that some of the random variables X 1 , X 2 , ⋯ , X n can be observed and denote by the maximum of the observed random variables from the set { X 1 , X 2 , ⋯ ,...

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Bibliographic Details
Published in:Extremes (Boston) 2012-09, Vol.15 (3), p.319-332
Main Authors: Tan, Zhongquan, Wang, Yuebao
Format: Article
Language:English
Subjects:
Air pollution
Asymptotic methods
Civil Engineering
Economics
Environmental Management
Finance
Hydrogeology
Insurance
Management
Mathematical models
Mathematics and Statistics
Quality Control
Random variables
Reliability
Safety and Risk
Statistics
Statistics for Business
Theory
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Summary:Let X 1 , X 2 , ⋯ be a sequence of independent and identically distributed random variables and M n  =  max { X 1 , X 2 , ⋯ , X n }. Suppose that some of the random variables X 1 , X 2 , ⋯ , X n can be observed and denote by the maximum of the observed random variables from the set { X 1 , X 2 , ⋯ , X n }. The limiting distribution of random vector is derived. The result is also extended to the case of stationary Gaussian sequences. In the end, the almost sure limit theorem on for a sequence of independent and identically distributed random variables is proved.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-011-0140-z