Certain bivariate distributions and random processes connected with maxima and minima
Author
Summary, in English
It is well-known that [S(x)]^n and [F(x)]^n are the survival function and the
distribution function of the minimum and the maximum of n independent, identically distributed random variables, where S and F are their common survival and distribution functions, respectively. These two extreme order statistics play important role in countless applications, and are the central and well-studied objects of extreme value theory. In this work we provide stochastic representations for the quantities [S(x)]^alpha and [F(x)]^beta, where alpha> 0 is no longer an integer, and construct a bivariate model with these margins. Our constructions and representations involve maxima and minima with a random number of terms. We also discuss generalizations to random process and further extensions.
distribution function of the minimum and the maximum of n independent, identically distributed random variables, where S and F are their common survival and distribution functions, respectively. These two extreme order statistics play important role in countless applications, and are the central and well-studied objects of extreme value theory. In this work we provide stochastic representations for the quantities [S(x)]^alpha and [F(x)]^beta, where alpha> 0 is no longer an integer, and construct a bivariate model with these margins. Our constructions and representations involve maxima and minima with a random number of terms. We also discuss generalizations to random process and further extensions.
Department/s
Publishing year
2016
Language
English
Publication/Series
Working Papers in Statistics
Issue
2016:9
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Document type
Working paper
Publisher
Department of Statistics, Lund university
Topic
- Probability Theory and Statistics
Keywords
- Copula
- distribution theory
- exponentiated distribution
- extremes
- generalized exponential distribution
- order statistics
- random minimum
- random maximum
- Sibuya distribution
Status
Published