An alternative discrete skew Laplace distribution

In this paper, an alternative discrete skew Laplace distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The distribution’s properties are explored and it is compared to a Laplace distribution on integers recently proposed in the literature. The issues related to the sample estimation of its parameters are discussed, with a particular focus on the maximum likelihood method and large-sample confidence intervals based on Fisher’s information matrix; a modified version of the method of moments is presented along with the method of proportion, which is particularly suitable for such a discrete model. Two hypothesis tests are suggested. A Monte Carlo simulation study is carried out to assess the statistical properties of these inferential techniques. Applications of the proposed model to real data are given as well.