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A generalized Sibuya distribution

Kozubowski, Tomasz J and Podgórski, Krzysztof LU (2017) In Annals of the Institute of Statistical Mathematics
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
organization
publishing date
type
Contribution to journal
publication status
epub
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
pages
33 pages
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
2017-08-07 10:41:56
@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},
  keyword      = {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},
  month        = {06},
  pages        = {33},
  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},
  year         = {2017},
}