# Lund University Publications

## LUND UNIVERSITY LIBRARIES

(2016) In Working Papers in Statistics
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 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.
author
organization
publishing date
type
Working Paper
publication status
published
subject
in
Working Papers in Statistics
issue
2016:8
pages
27 pages
publisher
Department of Statistics, Lund university
language
English
LU publication?
yes
id
93211cd6-2790-4290-a3b7-12383b18b74c
2016-09-21 10:12:38
date last changed
2016-09-21 10:12:38
```@misc{93211cd6-2790-4290-a3b7-12383b18b74c,
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 is obtained as the distribution of the excess random variable N − k given    N &gt; 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.},
author       = {Kozubowski, Tomasz J and Podgórski, Krzysztof},
language     = {eng},
number       = {2016:8},
pages        = {27},
publisher    = {ARRAY(0xa344c18)},
series       = {Working Papers in Statistics},
title        = {A generalized Sibuya distribution},
year         = {2016},
}

```