A generalized Sibuya distribution

Research output: Contribution to journalArticle


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.


External organisations
  • University of Nevada, Reno
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics


  • Discrete Pareto distribution, Distribution theory, Extreme value theory, Infinite divisibility, Mixed Poisson process, Power law, Pure death process, Records, Yule distribution, Zipf’s law
Original languageEnglish
Number of pages33
JournalAnnals of the Institute of Statistical Mathematics
StateE-pub ahead of print - 2017 Jun 22

Related research output

Kozubowski, T. J. & Krzysztof Podgórski 2016 Department of Statistics, Lund university, 27 p.(Working Papers in Statistics; no. 2016:8)

Research output: Working paper

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