The Lomax regression model with residual analysis: an application to insurance data

Area of Science:

• Statistics
• Econometrics
• Survival Analysis

Background:

• The gamma regression model is widely used for modeling positive, skewed data.
• Limitations of the gamma model may necessitate alternative approaches for specific datasets.
• Regression modeling is crucial in insurance for risk assessment and pricing.

Purpose of the Study:

• Introduce and evaluate the novel Lomax regression model.
• Compare the performance of the Lomax regression model against the established gamma regression model.
• Demonstrate the practical utility of the Lomax regression model using real-world insurance data.

Main Methods:

• Parameter estimation using the maximum-likelihood method.
• Finite sample performance assessment via Monte-Carlo simulation studies.
• Model adequacy checking using randomized quantile residuals.

Main Results:

• The Lomax regression model is presented as a viable alternative to the gamma regression model.
• Simulation results indicate the performance characteristics of the maximum-likelihood estimation for the Lomax model.
• Residual analysis supports the adequacy of the fitted Lomax regression model.

Conclusions:

• The Lomax regression model offers a valuable alternative for regression analysis, particularly in insurance contexts.
• The proposed model demonstrates practical usefulness and statistical adequacy.
• Further research can explore extensions and applications of the Lomax regression model.