An extended Rayleigh Weibull model with actuarial measures and applications

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The Rayleigh-Weibull distribution is a flexible model for lifetime data.
• The Marshall-Olkin family of distributions offers a method for creating new, more flexible distributions.
• There is a need for advanced statistical models in reliability and actuarial science.

Purpose of the Study:

• To propose and analyze a new statistical model, the Marshall-Olkin-Rayleigh-Weibull (MORW) distribution.
• To derive and discuss various mathematical and statistical properties of the MORW distribution.
• To evaluate the performance of different parameter estimation methods for the MORW model and demonstrate its practical utility.

Main Methods:

• Extension of the Rayleigh-Weibull model using the Marshall-Olkin family.
• Derivation of analytical expressions for quantiles, moments, entropy, and order statistics.
• Monte Carlo simulation to assess estimator performance.
• Calculation of actuarial measures like Value-at-Risk and expected shortfall.
• Application to real-world datasets for validation.

Main Results:

• Explicit formulas for key statistical properties of the MORW distribution were derived.
• A comprehensive comparison of six estimation methods was performed via simulation.
• The MORW model demonstrated applicability and usefulness on real data.
• Actuarial measures were computed, highlighting potential applications in risk management.

Conclusions:

• The proposed Marshall-Olkin-Rayleigh-Weibull (MORW) distribution is a valuable addition to the statistical modeling toolkit.
• The study provides a thorough theoretical and empirical evaluation of the MORW model.
• The MORW distribution shows promise for applications in reliability, actuarial science, and other fields requiring flexible lifetime modeling.