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.