Krzysztof Podgórski
Professor, Head of the Department of Statistics
Transmuted distributions and random extrema
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 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.
Department/s
- Department of Statistics
Publishing year
2016-09-01
Language
English
Pages
6-8
Publication/Series
Statistics and Probability Letters
Volume
116
Document type
Journal article
Publisher
Elsevier
Topic
- Probability Theory and Statistics
Keywords
- Distribution theory
- Extremes
- Marshall-Olkin generalized distribution
- Quadratic transmutation map
- Random extrema
- Stochastic representation
Status
Published
ISBN/ISSN/Other
- ISSN: 0167-7152