International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 25, Pages 1563-1575

Circular Polya distributions of order k

Gregory A. Tripsiannis1 and Andreas N. Philippou2

1Department of Medical Statistics, Faculty of Medicine, Democritus University of Thrace, Alexandroupolis 68100, Greece
2Department of Mathematics, University of Patras, Patras 26500, Greece

Received 10 October 2002

Copyright © 2003 Gregory A. Tripsiannis and Andreas N. Philippou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two circular Polya distributions of order k are derived by means of generalized urn models and by compounding, respectively, the type I and type II circular binomial distributions of order k of 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 order k.