A generalized Sibuya distribution
(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.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/19c4b41bb46247cf9fb51457d7adea17
 author
 Kozubowski, Tomasz J and Podgórski, Krzysztof ^{LU}
 organization
 publishing date
 20170622
 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
 00203157
 DOI
 10.1007/s1046301706113
 language
 English
 LU publication?
 yes
 id
 19c4b41bb46247cf9fb51457d7adea17
 date added to LUP
 20170711 13:09:07
 date last changed
 20170807 10:41:56
@article{19c4b41bb46247cf9fb51457d7adea17, 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 = {00203157}, 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/s1046301706113}, year = {2017}, }