The Skew-Symmetric-Laplace-Uniform Distribution

Abstract

The Laplace distribution is popular in the fields of economics and finance; however, empirical data often exhibit asymmetry and boundedness on one side of the support, features that the Laplace distribution fails to capture. To address this limitation, we propose a new family of skewed distributions using the skewing mechanism of Azzalini^[1], namely, the skew-symmetric-Laplace-uniform distribution (SSLUD). In this formulation, the uniform distribution serves a dual role by introducing skewness into the Laplace distribution and simultaneously restricting the distribution’s support to one side of the real line. This article provides a comprehensive description of the essential distributional properties of SSLUD. Estimators of the parameter are obtained using the method of moments under the permissible range of the parameter and the method of maximum likelihood. The finite sample and asymptotic properties of these estimators are studied using simulation. It is observed that the maximum likelihood estimator performs better than the constrained moment estimator, as demonstrated through a simulation study. Finally, the practical applicability of the proposed model is illustrated using real-world data comprising 348 automobile bodily injury log-claim amounts, and its performance is compared with that of standard competing distributions.

AMS Subject Classification: 62E10, 62F10