A New Type of Discrete Self-Decomposability and Its Application to Continuous-Time Markov Processes for Modeling Count Data Time Series
Authors:
- 5 January 2003
- journal article
- Published by Taylor & Francis in Stochastic Models
- Vol. 19 (2) , 235-254
Abstract
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.Keywords
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