Modeling Data with Nonlinear LogNormal–Pareto Regression via the Approximate Bayesian Computation

The development of regression models for composite distributions has received insufficient attention in the literature. The purpose of this research is to provide maximum likelihood (ML) and approximate Bayesian computation (ABC) estimators for the parameters of a regression model with a response variable following the LogNormal–Pareto composite distribution. Composite models such as Exponential–Pareto, LogNormal–Pareto, and Inverse-Gamma–Pareto, which separate small-to-moderate and significant losses using a threshold parameter, have been developed using classical and Bayesian methods and applied to insurance data. We derive closed-form formulas for MLEs in regression models with two and three covariates. For models with more than three covariates, we provide MLEs using Mathematica code. Simulation studies show that the ABC method is more accurate than the ML method. Mathematica code written specifically for the computations of the proposed methods is provided.