Discrete Probability Models Using Taylor Series Mohammad Masjed-Jamei, Edward Omey,

Meitner Cadena, Nasser Saad

We briefly consider basic properties of power series distribution and derive generating functions, Laplace transforms and combinations of such distributions. In the main section of the paper, we also study compound processes for sums and for extremes. We then provide new Panjer type of relationships and study the asymptotic behaviour of the compound processes. This analysis shows that these distributions may be used for modeling discrete data with light as well as heavy tails.