UNSPECIFIED (1993) ON THE EMPTY CELLS OF POISSON HISTOGRAMS. JOURNAL OF APPLIED PROBABILITY, 30 (3). pp. 561-574. ISSN 0021-9002

Full text not available from this repository.

Abstract

This paper considers the histogram of unit cell size built up from m independent observations on a Poisson (mu) distribution. The following question is addressed: what is the limiting probability of the event that there are no unoccupied cells lying to the left of occupied cells of the histogram? It is shown thal the probability of there being no such isolated empty cells (or isolated finite groups of empty cells) tends to unity as the number m of observations tends to infinity, but that the corresponding almost sure convergence fails. Moreover this probability does not tend to unity when the Poisson distribution is replaced by the negative binomial distribution arising when mu is randomized by a gamma distribution. The relevance to empirical Bayes statistical methods is discussed. AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 60 D05 SECONDARY 62 C12; 62 F12

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	JOURNAL OF APPLIED PROBABILITY
Publisher:	APPLIED PROBABILITY TRUST
ISSN:	0021-9002
Date:	September 1993
Volume:	30
Number:	3
Number of Pages:	14
Page Range:	pp. 561-574
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/21055

Data sourced from Thomson Reuters' Web of Knowledge

Request changes to a record

Actions (login required)

View Item