Bimodal Power Laplace Distribution

Abstract

This article has two purposes. The first (main) goal is to introduce a new flexible distribution defined in an infinite domain. The distribution in question is named the bimodal power Laplace distribution. The second (additional) goal is a chronological overview of distributions belonging to the large family of Laplace distributions. Some properties of the BPL such as PDF, CDF, modal values, inflection points, quantiles, moments, Moors' measure, moments of order statistics and instructions to generate pseudo-random numbers are presented. The unknown parameters of the new distribution are estimated by the maximum likelihood method. The Shannon, Tsallis and Renyi entropies and Fisher Information Matrix are also presented. Illustrative examples of applicability and flexibility of the introduced distributions are given. The most important R codes and proofs of some theorems are given in the Appendix.