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Portrait of Krzysztof Podgórski. Photo.

Krzysztof Podgórski

Professor, Head of the Department of Statistics

Portrait of Krzysztof Podgórski. Photo.

A generalized Sibuya distribution

Author

  • Tomasz J Kozubowski
  • Krzysztof Podgórski

Summary, in English

The Sibuya distribution arises as the distribution of the waiting time for the first success in Bernoulli trials, where the probabilities of success are inversely proportional to the number of a trial. We study a generalization that can be viewed as the distribution of the excess random variable (Formula presented.) given (Formula presented.), where N has the Sibuya distribution and k is an integer. We summarize basic facts regarding this distribution and provide several new results and characterizations, shedding more light on its origin and possible applications. In particular, we emphasize the role Sibuya distribution plays in the extreme value theory and point out its invariance property with respect to random thinning operation.

Department/s

  • Department of Statistics

Publishing year

2018

Language

English

Pages

855-887

Publication/Series

Annals of the Institute of Statistical Mathematics

Volume

70

Issue

4

Document type

Journal article

Publisher

Springer

Topic

  • Probability Theory and Statistics

Keywords

  • Discrete Pareto distribution
  • Distribution theory
  • Extreme value theory
  • Infinite divisibility
  • Mixed Poisson process
  • Power law
  • Pure death process
  • Records
  • Yule distribution
  • Zipf’s law

Status

Published

ISBN/ISSN/Other

  • ISSN: 0020-3157