In this paper, we further investigate stochastic comparisons of the lifetime of parallel systems with heterogeneous independent Pareto components in term of the star order and convex order. It will be proved that the lifetime of a parallel system with heterogeneous independent components from Pareto model is always smaller than from the lifetime of another parallel system with homogeneous independent components from Pareto model in the sense of convex order. Also, under a general condition on the scale parameters, it is proved a result involving with star order.

One of the most critical discussions in regression models is the selection of the optimal model, by identifying critical explanatory variables and negligible variables and more easily express the relationship between the response variable and explanatory variables. Given the limitations of selecting variables in classical methods, such as stepwise selection, it is possible to use penalized regression methods. One of the penalized regression models is the Lasso regression model, in which it is assumed that errors follow a normal distribution. In this paper, we introduce the Bayesian Lasso regression model with an asymmetric distribution error and the high dimensional setting. Then, using the simulation studies and real data analysis, the performance of the proposed model's performance is discussed.