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A generalized Sibuya distribution

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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 is obtained as the distribution of the excess random variable N − k given N > k, where N has the Sibuya distribution. 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.

Publishing year

2016

Language

English

Publication/Series

Working Papers in Statistics

Issue

2016:8

Document type

Working paper

Publisher

Department of Statistics, Lund university

Topic

  • Probability Theory and Statistics

Status

Published