On the Burr XII-moment exponential distribution

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Lifetime data analysis is crucial in various fields.
• Existing statistical models may lack the flexibility to capture complex failure patterns.
• The Burr XII distribution is a known flexible model, but extensions are needed.

Purpose of the Study:

• Introduce a new flexible lifetime model: the Burr XII moment exponential (BXII-ME) distribution.
• Derive key mathematical and reliability properties of the BXII-ME distribution.
• Evaluate the performance of different parameter estimation techniques for the BXII-ME model.

Main Methods:

• Mathematical derivations of moments and reliability measures.
• Application of Maximum Likelihood, Maximum Product Spacings, Least Squares, Weighted Least Squares, Cramer-von Mises, and Anderson-Darling estimation methods.
• Simulation studies to assess estimator performance using graphical analysis.

Main Results:

• The BXII-ME distribution was successfully introduced and its properties derived.
• Various estimation methods were applied and their performance evaluated through simulations.
• The BXII-ME model demonstrated potential in analyzing real-world data.

Conclusions:

• The BXII-ME distribution provides a valuable addition to flexible lifetime models.
• The study validates the utility of multiple estimation techniques for the BXII-ME distribution.
• The model's applicability is confirmed through analyses of tax revenue and fatigue life data.