| Abstract | We propose a family of extended thinning operators, indexed by a parameter gamma in [0, 1), with the boundary case of gamma = 0 corresponding to the well-known binomial thinning operator. The extended thinning operators can be used to construct a class of continuous-time Markov processes for modeling count time series data. The class of stationary distributions of these processes is called generalized discrete self-decomposable, denoted by DSD (gamma). We obtain characterization results for the DSD (gamma) class and investigate relationships among the classes for different gamma's. |
