A new autoregressive process with Marshall-Olkin new Pareto-type (MOPT) marginal distribution is recommended in this paper. The distribution of the extremes with closure property, estimation via the maximum likelihood technique, and model fitting to the breakdown time of a particular type of electrical insulating material stressed under steady voltage are some of the statistical frameworks of the MOPT distribution, which are discussed comprehensively. The last aspect of the paper is devoted to the order max-autoregressive process based on the MOPT marginal distribution, showing its Pegram representation, along with the statistical properties and the estimation of the unknown parameters of the process. Moreover, the model is utilized for time series data and compared to some competitive models under a yearly alcohol consumption from 1995 to 2019 obtained from New Zealand.
