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A generalized Sibuya distribution

In English

Författare

Summary, in English

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 is obtained as the distribution of the excess random variable N − k given N > k, where N has the Sibuya distribution. 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.

Publiceringsår

2016

Språk

Engelska

Publikation/Tidskrift/Serie

Working Papers in Statistics

Issue

2016:8

Dokumenttyp

Working paper

Förlag

Department of Statistics, Lund university

Ämne

  • Probability Theory and Statistics

Status

Published