Transmuted distributions and random extrema
(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
- Kozubowski, Tomasz J. and Podgórski, Krzysztof LU
- organization
- publishing date
- 2016-09-01
- 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
-
- wos:000378963700002
- scopus:84973098227
- 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
- 2024-06-14 18:49:42
@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}},
keywords = {{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}},
doi = {{10.1016/j.spl.2016.04.001}},
volume = {{116}},
year = {{2016}},
}