Estimation and goodness-of-fit testing for non-negative random variables with explicit Laplace transform

TL;DR

This paper introduces a Laplace transform-based method for parameter estimation and goodness-of-fit testing of positive random variables, especially useful when density functions are complex or unavailable.

Contribution

It develops a novel, data-driven inferential approach leveraging Laplace transforms, with proven large-sample properties and practical implementation for specific distributions.

Findings

Good finite-sample performance demonstrated in Monte Carlo simulations

Method effectively applied to positive stable and Tweedie distributions

Provides a new tool for modeling positive random variables with complex densities

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.