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This study introduces a new statistical model, the generalized Marshall-Olkin exponentiated exponential distribution. It explores its properties and estimation methods, demonstrating its real-world applicability.

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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.