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Run Statistics Defined on the Multicolor URN Model

Part of: Distribution theory Combinatorial probability

Published online by Cambridge University Press:  14 July 2016

Serkan Eryilmaz
Serkan Eryilmaz*
Affiliation:
Izmir University of Economics
*
∗Postal address: Izmir University of Economics, Department of Mathematics, 35330 Izmir, Turkey. Email address: [email protected]
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Abstract

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Recently, Makri, Philippou and Psillakis (2007b) studied the exact distribution of success run statistics defined on an urn model. They derived the exact distributions of various success run statistics for a sequence of binary trials generated by the Pólya-Eggenberger sampling scheme. In our study we derive the joint distributions of run statistics defined on the multicolor urn model using a simple unified combinatorial approach and extend some of the results of Makri, Philippou and Psillakis (2007b). As a consequence of our results, we obtain the joint distributions of success and failure runs defined on the two-color urn model. The results enable us to compute the characteristics of particular consecutive-type systems and start-up demonstration tests.

Keywords

Consecutive-k,r-out-of-n: DFM systemDirichlet measuremulticolor Polya sampling schememultistate exchangeable trialrunsstart-up demonstration testwaiting time

MSC classification

Secondary: 60C05: Combinatorial probability 62E15: Exact distribution theory
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1007 - 1023
Copyright
Copyright © Applied Probability Trust 2008 

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