The circular Gamma distribution and wrapped sums of independent Gamma distributions
by
Carlos A. Coelho
The New University of Lisbon - Faculty of Science and Technology - Mathematics Department

We first obtain an expression for the probability density function of the wrapped or circular Gamma distribution and then we show how it may be seen, for both integer and non-integer shape parameter, as a mixture of truncated Gamma distributions. Some other properties of the wrapped Gamma distribution are studied and it is shown how this distribution and namely mixtures of these distributions may be a much useful tool in modelling directional data in biology and meteorology. Based on the results obtained, namely the ones concerning mixtures, and on some properties of the distributions of the sum of independent Gamma random variables, the wrapped distribution of such sums, for both integer and non-integer shape parameters are derived. Also the wrapped sum of independent generalized Laplace distributions is introduced as a particular case of a mixture of wrapped Gamma distributions. Among the particular cases of the distributions introduced there are symmetrical, slightly skewed and highly skewed wrapped distributions as well as the recently introduced wrapped Exponential and Laplace distributions.

Date received: October 31, 2005

Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # carr-34.