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Transmuted distributions and extrema of random number of variables

Kozubowski, Tomasz J. and Podgórski, Krzysztof LU (2016) In Working Papers in Statistics
Abstract
Recent years have seen an increased interest in the transmuted probability models,which arise from transforming a “base” distribution into its generalized counterpart. While many standard probability distributions were generalized throughout this simple construction, the concept lacked deeper theoretical interpretation. This note demonstrates that the scheme is more than just a simple trick to obtain a new cumulative distribution function. We show that the transmuted distributions can be viewed as the distribution of maxima (or minima) of a random number N of independent and identically distributed variables with the base distribution, where N has a Bernoulli distribution shifted up by one. Consequently, the transmuted models are, in fact,... (More)
Recent years have seen an increased interest in the transmuted probability models,which arise from transforming a “base” distribution into its generalized counterpart. While many standard probability distributions were generalized throughout this simple construction, the concept lacked deeper theoretical interpretation. This note demonstrates that the scheme is more than just a simple trick to obtain a new cumulative distribution function. We show that the transmuted distributions can be viewed as the distribution of maxima (or minima) of a random number N of independent and identically distributed variables with the base distribution, where N has a Bernoulli distribution shifted up by one. Consequently, the transmuted models are, in fact, only a special case of extremal distributions defined through a more general N .
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author
organization
publishing date
type
Working Paper
publication status
published
subject
in
Working Papers in Statistics
issue
2016:6
pages
8 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
2ef4fcc4-ae44-45e0-90f9-b0c0a2536882
date added to LUP
2016-09-21 11:54:54
date last changed
2016-09-21 11:56:28
@misc{2ef4fcc4-ae44-45e0-90f9-b0c0a2536882,
  abstract     = {Recent years have seen an increased interest in the transmuted probability models,which arise from transforming a “base” distribution into its generalized counterpart. While many standard probability distributions were generalized throughout this simple construction, the concept lacked deeper theoretical interpretation. This note demonstrates that the scheme is more than just a simple trick to obtain a new cumulative distribution function. We show that the transmuted distributions can be viewed as the distribution of maxima (or minima) of a random number N of independent and identically distributed variables with the base distribution, where N has a Bernoulli distribution shifted up by one. Consequently, the transmuted models are, in fact, only a special case of extremal distributions defined through a more general N .<br/>},
  author       = {Kozubowski, Tomasz J. and Podgórski, Krzysztof},
  language     = {eng},
  note         = {Working Paper},
  number       = {2016:6},
  pages        = {8},
  publisher    = {Department of Statistics, Lund university},
  series       = {Working Papers in Statistics},
  title        = {Transmuted distributions and extrema of random number of variables},
  year         = {2016},
}