A generalized Sibuya distribution
(2016) In Working Papers in Statistics- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/93211cd6-2790-4290-a3b7-12383b18b74c
- author
- Kozubowski, Tomasz J and Podgórski, Krzysztof LU
- organization
- publishing date
- 2016
- type
- Working paper/Preprint
- publication status
- published
- subject
- in
- Working Papers in Statistics
- issue
- 2016:8
- pages
- 27 pages
- publisher
- Department of Statistics, Lund university
- language
- English
- LU publication?
- yes
- id
- 93211cd6-2790-4290-a3b7-12383b18b74c
- date added to LUP
- 2016-09-21 10:12:38
- date last changed
- 2018-11-21 21:26:00
@misc{93211cd6-2790-4290-a3b7-12383b18b74c, 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.}}, author = {{Kozubowski, Tomasz J and Podgórski, Krzysztof}}, language = {{eng}}, note = {{Working Paper}}, number = {{2016:8}}, publisher = {{Department of Statistics, Lund university}}, series = {{Working Papers in Statistics}}, title = {{A generalized Sibuya distribution}}, url = {{https://lup.lub.lu.se/search/files/12779909/16162_41336_1_SM.pdf}}, year = {{2016}}, }