A new type of discrete self-decomposability and its application to continuous-time Markov processes for modeling count data time series

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A new type of discrete self-decomposability and its application to continuous-time Markov processes for modeling count data time series

TitleA new type of discrete self-decomposability and its application to continuous-time Markov processes for modeling count data time series
Publication TypeJournal Article
Year of Publication2003
AuthorsZhu, R, Joe, H
JournalStochastic Models
Volume19
Pagination235-254
ISSN1532-6349
AbstractWe 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.
DOI10.1081/STM-120020388