Run Statistics Defined on the Multicolor Urn Model

Abstract

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 Polya-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.