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The wrapped Gamma distribution and wrapped sums and linear combinations of independent Gamma and Laplace distributions

  • Carlos A. Coelho
Article

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 skewed and highly skewed wrapped distributions as well as the recently introduced wrapped Exponential and Laplace distributions.

Keywords

mixtures truncated Gamma distributions circular data circular distributions wrapped symmetrical and skew distributions 

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References

  1. Coelho, C. A., 1998. The generalized integer Gamma distribution — a basis for distributions in multivariate analysis. Journal of Multivariate Analysis 64, 86–102.MathSciNetCrossRefGoogle Scholar
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Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of Science and TechnologyThe New University of LisbonPortugal

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