摘要：In this article, we introduce a class of distributions that have heavy tails as compared to Pareto distribution of third kind, which we termed as Heavy Tailed Pareto (HP) distribution. Various structural properties of the new distribution are derived. It is shown that HP distribution is in the domain of attraction of minimum of Weibull distribution. A representation of HP distribution in terms of Weibull random variable is obtained. Two characterizations of HP distribution are obtained. The method of maximum likelihood is used for estimation of model parameters and simulation results are presented to assess the performance of new model. Marshall-Olkin Heavy Tailed Pareto (MOHP) distribution is also introduced and some of its properties are studied. It is shown that MOHP distribution is geometric extreme stable. An autoregressive time series model with the new model as marginal distribution is developed and its properties are studied.
关键词：autoregressive model; geometric extreme stability; Marshall–Olkin distribution autoregressive model; geometric extreme stability; Marshall–Olkin distribution
