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Abstract
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.
| Original language | English |
|---|---|
| Publisher | Department of Statistics, Lund university |
| Number of pages | 27 |
| Publication status | Published - 2016 |
Publication series
| Name | Working Papers in Statistics |
|---|---|
| Publisher | Department of Statistics, Lund University |
| No. | 2016:8 |
Subject classification (UKÄ)
- Probability Theory and Statistics
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A generalized Sibuya distribution
Kozubowski, T. J. & Podgórski, K., 2018, In: Annals of the Institute of Statistical Mathematics. 70, 4, p. 855-887Research output: Contribution to journal › Article › peer-review