Krzysztof Podgórski
Professor, Head of the Department of Statistics
Transmuted distributions and extrema of random number of variables
Author
Summary, in English
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 .
Department/s
- Department of Statistics
Publishing year
2016
Language
English
Publication/Series
Working Papers in Statistics
Issue
2016:6
Full text
- Available as PDF - 395 kB
- Download statistics
Document type
Working paper
Publisher
Department of Statistics, Lund university
Topic
- Probability Theory and Statistics
Status
Published