Certain bivariate distributions and random processes connected with maxima and minima
(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:
http://lup.lub.lu.se/record/75d396f8-7067-474c-a25c-7f81bcdd3cd2
- author
- Kozubowski, Tomasz J and Podgórski, Krzysztof ^{LU}
- organization
- publishing date
- 2016
- 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
- 2018-11-21 21:26:12
@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> 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}, note = {Working Paper}, number = {2016:9}, pages = {24}, publisher = {Department of Statistics, Lund university}, series = {Working Papers in Statistics}, title = {Certain bivariate distributions and random processes connected with maxima and minima}, year = {2016}, }