Transmuted distributions and extrema of random number of variables
(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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Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/2ef4fcc4-ae44-45e0-90f9-b0c0a2536882
- author
- Kozubowski, Tomasz J. and Podgórski, Krzysztof ^{LU}
- organization
- publishing date
- 2016
- 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}, number = {2016:6}, pages = {8}, publisher = {ARRAY(0x94d6788)}, series = {Working Papers in Statistics}, title = {Transmuted distributions and extrema of random number of variables}, year = {2016}, }