Estimation and goodness-of-fit testing for non-negative random variables with explicit Laplace transform
Abstract
Many flexible families of positive random variables exhibit non-closed forms of the density and distribution functions and this feature is considered unappealing for modelling purposes. However, such families are often characterized by a simple expression of the corresponding Laplace transform. Relying on the Laplace transform, we propose to carry out parameter estimation and goodness-of-fit testing for a general class of non-standard laws. We suggest a novel data-driven inferential technique, providing parameter estimators and goodness-of-fit tests, whose large-sample properties are derived. The implementation of the method is specifically considered for the positive stable and Tweedie distributions. A Monte Carlo study shows good finite-sample performance of the proposed technique for such laws.
Cite
@article{arxiv.2405.15041,
title = {Estimation and goodness-of-fit testing for non-negative random variables with explicit Laplace transform},
author = {Lucio Barabesi and Antonio Di Noia and Marzia Marcheselli and Caterina Pisani and Luca Pratelli},
journal= {arXiv preprint arXiv:2405.15041},
year = {2025}
}