On the Marshall-Olkin Extended Gamma Lindley autoregressive process

Abstract

In this research paper, we generalize the Gamma Lindley distribution according to the Marshall-Olkin transformation, in order to enhance data modeling flexibility. The r th moment of this distribution is derived. Hence, we develop a first autoregressive process (Xn)n∈N with minification structure using the proposed model. We compute the first order autocovariance function. We prove that P(Xn+1 = Xn) > 0, then we derive explicitly the joint probability distribution of (Xn, Xn+1). Consequently, we conduct a statistical inference for the unknown parameters of this process using maximum likelihood estimation approach. We apply the proposed autoregressive process to predict a time series real data and we prove that it is a good predictive model compared with the standard form for the first order autoregressive model.