Marshall-Olkin Generalized Asymmetric Laplace distributions and processes

The Marshall-Olkin Generalised Asymmetric Laplace distribution is introduced and studied. An approximation is made and various properties including self decomposability, geometric infinite divisibility, limit properties etc.are established. Two autoregressive processes namely model I and model II are developed and studied. The sample path properties are explored for various parameter combinations. The distribution of sums, joint distribution of contiguous observations of the process, etc are obtained. The model is extended to kth order also.Parameters are estimated by the method of maximum likelihood and a real data on gold prices is fitted to the new model.