Krzysztof Podgórski
Professor, Head of the Department of Statistics
A generalized Sibuya distribution
Author
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