A novel M-Lognormal-Burr regression model with varying threshold for modeling heavy-tailed claim severity data

Area of Science:

• Statistics
• Actuarial Science
• Probability Theory

Background:

• Accurate modeling of insurance claim severity is crucial for risk management.
• Traditional distributions may not fully capture the complexities of diverse loss data.
• Composite probability distributions offer a flexible framework for modeling heterogeneous data.

Purpose of the Study:

• To introduce a novel composite Lognormal-Burr distribution family.
• To develop a composite regression model for claim severity data.
• To demonstrate the practical application and effectiveness of the proposed model.

Main Methods:

• Development of a novel composite Lognormal-Burr distribution using the Mode-Matching technique.
• Construction of a composite regression model incorporating the new distribution.
• Parameter estimation methods for precise model calibration.

Main Results:

• The proposed composite Lognormal-Burr distribution effectively models claim severity data.
• The composite regression model demonstrates capability in addressing diverse policyholder risk characteristics.
• Validation using real-world insurance data confirms the model's practical utility.

Conclusions:

• Composite probability distributions, specifically the Lognormal-Burr family, provide a powerful tool for claim severity modeling.
• The developed composite regression model offers an effective approach for actuarial analysis.
• The study highlights the importance of advanced statistical methods in insurance risk assessment.