The Wrapped Gamma Distribution and Wrapped Sums and Linear Combinations of Independent Gamma and Laplace Distributions

Abstract

Abstract In this paper 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, both for 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 mixtures of these distributions may be much useful tools 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 versions of the distributions 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 ske...