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Certain bivariate distributions and random processes connected with maxima and minima

Kozubowski, Tomasz J and Podgórski, Krzysztof LU (2016) In Working Papers in Statistics
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Working Paper
publication status
published
subject
keywords
Copula, distribution theory, exponentiated distribution, extremes, generalized exponential distribution, order statistics, random minimum, random maximum, Sibuya distribution
in
Working Papers in Statistics
issue
2016:9
pages
24 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
75d396f8-7067-474c-a25c-7f81bcdd3cd2
alternative location
http://journals.lub.lu.se/index.php/stat/article/view/16183
date added to LUP
2016-09-27 12:09:50
date last changed
2016-09-27 12:09:50
@misc{75d396f8-7067-474c-a25c-7f81bcdd3cd2,
  abstract     = {It is well-known that [S(x)]^n and [F(x)]^n are the survival function and the<br>
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&gt; 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.},
  author       = {Kozubowski, Tomasz J and Podgórski, Krzysztof},
  keyword      = {Copula,distribution theory,exponentiated distribution,extremes,generalized exponential distribution,order statistics,random minimum,random maximum,Sibuya distribution},
  language     = {eng},
  number       = {2016:9},
  pages        = {24},
  publisher    = {ARRAY(0x925cb80)},
  series       = {Working Papers in Statistics},
  title        = {Certain bivariate distributions and random processes connected with maxima and minima},
  year         = {2016},
}