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Certain bivariate distributions and random processes connected with maxima and minima

In English

Författare

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.

Publiceringsår

2016

Språk

Engelska

Publikation/Tidskrift/Serie

Working Papers in Statistics

Issue

2016:9

Dokumenttyp

Working paper

Förlag

Department of Statistics, Lund university

Ämne

  • Probability Theory and Statistics

Nyckelord

  • Copula
  • distribution theory
  • exponentiated distribution
  • extremes
  • generalized exponential distribution
  • order statistics
  • random minimum
  • random maximum
  • Sibuya distribution

Aktiv

Published