Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications.

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The generalized Marshall-Olkin distribution is a flexible framework for modeling.
• There is a need for new statistical distributions to capture complex data patterns.

Purpose of the Study:

• To propose and analyze a new statistical distribution: the generalized Marshall-Olkin exponentiated exponential distribution.
• To investigate the statistical properties and parameter estimation techniques for this new distribution.
• To demonstrate the practical utility of the proposed distribution through real-world data analysis.

Main Methods:

• Derivation of statistical properties including moments and generating functions.
• Development of five distinct parameter estimation methods (Maximum Likelihood, Least Squares, Weighted Least Squares, Anderson-Darling, Cramer-von Mises).
• Conducting a comprehensive Monte Carlo simulation study to evaluate estimator performance.
• Application of the distribution to four diverse real-world datasets.

Main Results:

• The proposed distribution exhibits valuable statistical characteristics.
• The developed estimation methods provide reliable parameter estimates.
• Simulation results indicate good finite sample properties for the estimators.
• Real data applications confirm the distribution's effectiveness and flexibility.

Conclusions:

• The generalized Marshall-Olkin exponentiated exponential distribution is a promising addition to statistical modeling.
• The study provides a robust framework for parameter estimation and validation.
• The distribution demonstrates significant potential for applications in various scientific and engineering fields.