A generalized Sibuya distribution

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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.

Detaljer

Författare
Enheter & grupper
Externa organisationer
  • University of Nevada, Reno
Forskningsområden

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Sannolikhetsteori och statistik

Nyckelord

Originalspråkengelska
Sidor (från-till)855-887
TidskriftAnnals of the Institute of Statistical Mathematics
Volym70
Utgåva nummer4
Tidigt onlinedatum2017 jun 22
StatusPublished - 2018
PublikationskategoriForskning
Peer review utfördJa

Relaterad forskningsoutput

Kozubowski, T. J. & Krzysztof Podgórski, 2016, Department of Statistics, Lund university, 27 s. (Working Papers in Statistics; nr. 2016:8).

Forskningsoutput: Working paper

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