Extending Approximate Bayesian Computation to Non-Linear Regression Models: The Case of Composite Distributions

Mostafa S. Aminzadeh () and Min Deng
Additional contact information
Mostafa S. Aminzadeh: Department of Mathematics, Towson University, Towson, MD 21252, USA
Min Deng: Department of Mathematics, Towson University, Towson, MD 21252, USA

Risks, 2025, vol. 13, issue 11, 1-17

Abstract: Modeling loss data is a crucial aspect of actuarial science. In the insurance industry, small claims occur frequently, while large claims are rare. Traditional heavy-tail distributions, such as Weibull, Log-Normal, and Inverse Gaussian distributions, are not suitable for describing insurance data, which often exhibit skewness and fat tails. The literature has explored classical and Bayesian inference methods for the parameters of composite distributions, such as the Exponential–Pareto, Weibull–Pareto, and Inverse Gamma–Pareto distributions. These models effectively separate small to moderate losses from significant losses using a threshold parameter. This research aims to introduce a new composite distribution, the Gamma–Pareto distribution with two parameters, and employ a numerical computational approach to find the maximum likelihood estimates (MLEs) of its parameters. A novel computational approach for a nonlinear regression model where the loss variable is distributed as the Gamma–Pareto and depends on multiple covariates is proposed. The maximum likelihood (ML) and Approximate Bayesian Computation (ABC) methods are used to estimate the regression parameters. The Fisher information matrix, along with a multivariate normal distribution as the prior distribution, is utilized through the ABC method. Simulation studies indicate that the ABC method outperforms the ML method in terms of accuracy.

Keywords: ML estimation; Approximate Bayesian Computation (ABC); Gamma-Pareto composite distribution; fisher information matrix; multivariate normal distribution; Wald’s test (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-9091/13/11/220/pdf (application/pdf)
https://www.mdpi.com/2227-9091/13/11/220/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:13:y:2025:i:11:p:220-:d:1787645

Access Statistics for this article

Risks is currently edited by Mr. Claude Zhang

More articles in Risks from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().