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Transmuted distributions and random extrema

Kozubowski, Tomasz J. and Podgórski, Krzysztof LU (2016) In Statistics and Probability Letters 116. p.6-8
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 construction, the concept lacked deeper theoretical interpretation. 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 a special case of extremal distributions defined through a more general N.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Distribution theory, Extremes, Marshall-Olkin generalized distribution, Quadratic transmutation map, Random extrema, Stochastic representation
in
Statistics and Probability Letters
volume
116
pages
3 pages
publisher
Elsevier
external identifiers
  • scopus:84973098227
  • wos:000378963700002
ISSN
0167-7152
DOI
10.1016/j.spl.2016.04.001
language
English
LU publication?
yes
id
1ec5999e-9583-44f8-8f85-5ad6af5faa71
date added to LUP
2016-11-28 14:05:53
date last changed
2017-04-21 10:44:23
@article{1ec5999e-9583-44f8-8f85-5ad6af5faa71,
  abstract     = {<p>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 construction, the concept lacked deeper theoretical interpretation. 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 a special case of extremal distributions defined through a more general N.</p>},
  author       = {Kozubowski, Tomasz J. and Podgórski, Krzysztof},
  issn         = {0167-7152},
  keyword      = {Distribution theory,Extremes,Marshall-Olkin generalized distribution,Quadratic transmutation map,Random extrema,Stochastic representation},
  language     = {eng},
  month        = {09},
  pages        = {6--8},
  publisher    = {Elsevier},
  series       = {Statistics and Probability Letters},
  title        = {Transmuted distributions and random extrema},
  url          = {http://dx.doi.org/10.1016/j.spl.2016.04.001},
  volume       = {116},
  year         = {2016},
}