Extremes of Stationary Sequences with Failures

Let {X n } be a stationary sequence subject to failures, meaning that some of the variables will be either withdrawn or somehow replaced. We discuss some extremal properties of three different failure models assuming that initially {X n } has an extremal index and satisfies appropriate dependence co...

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Bibliographic Details
Published inStochastic models Vol. 22; no. 3; pp. 537 - 557
Main Authors Hall, Andreia, Hüsler, Jürg
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Taylor & Francis Group 01.09.2006
Taylor & Francis
Subjects
Discrete distributions
Exact sciences and technology
Exceedance point processes
Extremal index
Extreme value theory
Failure
Limit theorems
Mathematics
Missing observation
Primary 60F05
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Secondary 60G70, 60G10, 60G55
Stochastic processes
Stochastic model
60G55
60G10
Probability theory
Failures
Care
Missing data
Stationary sequence
Discrete distribution
Point process
Extreme-value problems
Extremal index
Discrete distributions; Exceedance point processes; Extremal index; Extreme value theory; Failure; Missing observation. Primary 60F05; Secondary 60G70
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ISSN1532-6349
1532-4214
DOI10.1080/15326340600820554

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Summary:Let {X n } be a stationary sequence subject to failures, meaning that some of the variables will be either withdrawn or somehow replaced. We discuss some extremal properties of three different failure models assuming that initially {X n } has an extremal index and satisfies appropriate dependence conditions. Special care is taken whenever X n is integer valued.
ISSN:1532-6349
1532-4214
DOI:10.1080/15326340600820554