A generalized Sibuya distribution
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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 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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Research areas and keywords  Subject classification (UKÄ) – MANDATORY
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Original language  English 

Number of pages  33 
Journal  Annals of the Institute of Statistical Mathematics 
State  Epub ahead of print  2017 Jun 22 
Peerreviewed  Yes 
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Research output: Working paper