Circular Polya distributions of orderk

Gregory A Tripsiannis,Andreas N Philippou

doi:10.1155/s0161171203210553

Abstract

Two circular Polya distributions of orderkare derived by means of generalized urn models and by compounding, respectively, the type I and type II circular binomial distributions of orderkof Makri and Philippou (1994) with the beta distribution. It is noted that the above two distributions include, as special cases, new circular hypergeometric, negative hypergeometric, and discrete uniform distributions of the same order and type. The means of the new distributions are obtained and two asymptotic results are established relating them to the above-mentioned circular binomial distributions of orderk.

Highlights

In five pioneering papers, Philippou and Muwafi [18], Philippou et al [17], Philippou [14], and Philippou et al [15, 16] introduced the study of univariate and multivariate distributions of order k
Makri and Philippou [11] introduced two circular binomial distributions of order k, as the distribution of nonoverlapping and possibly overlapping success runs of length k in n Bernoulli trials arranged on a circle
The distribution of circular nonoverlapping or possibly overlapping success runs of length k was studied by Chryssaphinou et al [5], Koutras et al [9], Charalambides [4], and Koutras et al [10]

Summary

Introduction

Philippou and Muwafi [18], Philippou et al [17], Philippou [14], and Philippou et al [15, 16] introduced the study of univariate and multivariate distributions of order k. Makri and Philippou [11] introduced two circular binomial distributions of order k, as the distribution of nonoverlapping and possibly overlapping success runs of length k in n Bernoulli trials arranged on a circle.

Results

Conclusion