A generalized Sibuya distribution
(2018) In Annals of the Institute of Statistical Mathematics 70(4). p.855-887- 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 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.
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- author
- Kozubowski, Tomasz J and Podgórski, Krzysztof LU
- organization
- publishing date
- 2018
- type
- Contribution to journal
- publication status
- published
- subject
- 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
- in
- Annals of the Institute of Statistical Mathematics
- volume
- 70
- issue
- 4
- pages
- 855 - 887
- publisher
- Springer
- external identifiers
-
- scopus:85021052261
- ISSN
- 0020-3157
- DOI
- 10.1007/s10463-017-0611-3
- language
- English
- LU publication?
- yes
- id
- 19c4b41b-b462-47cf-9fb5-1457d7adea17
- date added to LUP
- 2017-07-11 13:09:07
- date last changed
- 2022-04-25 01:06:51
@article{19c4b41b-b462-47cf-9fb5-1457d7adea17, abstract = {{<p>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.</p>}}, author = {{Kozubowski, Tomasz J and Podgórski, Krzysztof}}, issn = {{0020-3157}}, 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}}, language = {{eng}}, number = {{4}}, pages = {{855--887}}, publisher = {{Springer}}, series = {{Annals of the Institute of Statistical Mathematics}}, title = {{A generalized Sibuya distribution}}, url = {{http://dx.doi.org/10.1007/s10463-017-0611-3}}, doi = {{10.1007/s10463-017-0611-3}}, volume = {{70}}, year = {{2018}}, }