A new class of extended Laplace distributions with applications to modeling contaminated Laplace data

Abstract

We introduce a new class of Extended Laplace (EL) distributions designed to characterize Laplace data influenced by independent uniform errors. We establish the fundamental theoretical properties of the model and develop both moment-based and maximum likelihood estimation (MLE) approaches for its parameters. Specifically, we present an effective iterative estimation scheme within the MLE framework to address optimization challenges arising from the complex structure of the domain. Our simulation results demonstrate the robustness of the estimation algorithms and the effectiveness of the EL model in handling imprecise Laplace data. Additionally, a real data example from the financial sector illustrates the broad modeling potential of this new distribution.