Zhang Shibin. An extension of the gamma and inverse Gaussian distributions. In: Jiang, Y., Li, J. (Eds.), Proceedings of Second International Conference on Modelling and Simulation 2009, 3: 396-401. (ISBN: 978-1-84626-063-6)

Abstract. Both the class of self-decomposable distributions and the class of compound Poisson distributions are subclasses of infinitely divisible distributions. They are a point of remarkable interest in fields of application such as finance and economics. For the familiar self-decomposable distributions (gamma and inverse Gaussian), we provide the explicit non-self-decomposable compound Poisson distributions, which made that the convolution between these two subclasses of distributions preserves self-decomposability.

Keywords: Self-decomposability, compound Poisson, process of Ornstein-Uhlenbeck type