First order integer-valued autoregressive model with a two-parameter generalized poisson-lindley distribution

Abstract

In this study, we introduce the first order integer-valued autoregressive models for count data with the two-parameter generalized Poisson-Lindley distribution. The thinning operators considered in this study are the binomial and negative binomial thinning operators. Some important probabilistic and statistical properties such as moments, stationarity and autocorrelation functions are derived. Moreover, parameter estimations and numerical simulations to examine the constructed model are performed. Finally, applications of the models for real data sets are also discussed.