A New Type of Discrete Self-Decomposability and Its Application to Continuous-Time Markov Processes for Modeling Count Data Time Series

We propose a family of extended thinning operators, indexed by a parameter γ in [0, 1), with the boundary case of γ=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 (γ). We obtain characterization results for the DSD (γ) class and investigate relationships among the classes for different γ's.