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Portrait of Krzysztof Podgórski. Photo.

Krzysztof Podgórski

Professor, Head of the Department of Statistics

Portrait of Krzysztof Podgórski. Photo.

Transmuted distributions and random extrema

Author

  • Tomasz J. Kozubowski
  • Krzysztof Podgórski

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