Skew Bimodal Power Laplace Distribution

Accepted - July 2025

Abstract

This article has two goals. The first (main) goal is to introduce a new flexible distribution defined in an infinite domain. This distribution is named the skew bimodal power Laplace distribution. The second (additional) goal is a chronological overview of distributions belonging to the large family of the skew Laplace distributions. Some properties of the proposal such as PDF, CDF, quantiles, generator, moments, skewness, kurtosis and moments of order statistics are presented. The unknown parameters of the new distribution are estimated by the maximum likelihood method. The Shannon entropy and Fisher Information Matrix are also presented. Illustrative examples of applicability and flexibility of the introduced distribution are given. The most important R codes and PDFs of distributions used in real data examples are given in the Appendix.