On a Generalized Alpha Skew Laplace Distribution: Properties and Applications

Abstract

This study introduces a novel extension of the alpha skew Laplace distribution  (Harandi and Alamatsaz 2013), designed to model datasets with both unimodal and bimodal characteristics effectively. A detailed examination of its statistical properties is conducted, including moments, moment-generating functions, cumulative distribution functions, and characterization results based on conditional distributions. The study also develops a location-scale generalization, enhancing the scope of the distribution for broader applications. Besides, parameter estimation is performed using maximum likelihood methods, supported by a comprehensive analysis of the Fisher Information Matrix, ensuring robust and precise inference.
The utility of the new distribution is validated through simulation studies which confirms the asymptotic consistency of its parameter estimates under varying sample sizes. Real-life applications involving white cell count data of Australian athletes and failure times of aircraft windshields demonstrate its superior performance over some established models. The newly introduced model consistently achieves lower Akaike and Bayesian Information Criteria (AIC/BIC) values, confirming its efficacy in fitting complex datasets. Additionally, likelihood ratio tests provide statistical evidence supporting its distinct advantages over nested models. This distribution represents a significant advancement in the field of probability and statistical modeling, offering a robust and versatile tool for analyzing diverse datasets with asymmetric or bimodal traits.