Asymmetric Uniform-Laplace Distribution‎: ‎Properties and Applications

The goal of this study is to introduce an Asymmetric Uniform-Laplace (AUL) distribution‎. ‎We present a detailed theoretical description of this distribution‎. ‎We try to estimate the parameters of AUL distribution using the maximum likelihood method‎. ‎Since the likelihood approach results in complicated forms‎, ‎we suggest a bootstrap-based approach for estimating the parameters‎. ‎The proposed method is mainly based on the shape of the empirical density‎. ‎We conduct a simulation study to assess the performance of the proposed procedure‎. ‎We also fit the AUL distribution to real data sets‎: ‎daily working time and Pontius data sets‎. ‎The results show that AUL distribution is a more appropriate choice than the Skew-Normal‎, ‎Skew t‎, ‎Asymmetric Laplace and Uniform-Normal distributions.