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This study introduces Ridge Regression for estimating the Lomax distribution shape parameter. Ridge Regression shows promising performance, outperforming Ordinary Least Squares in simulations.

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Area of Science:

  • Statistics
  • Probability Distributions

Background:

  • The Lomax distribution is frequently used in reliability and survival analysis.
  • Accurate estimation of its shape parameter is crucial for model performance.

Purpose of the Study:

  • To evaluate the Ridge Regression method for estimating the Lomax distribution shape parameter.
  • To compare Ridge Regression with classical and Bayesian estimation approaches.

Main Methods:

  • Ridge Regression was applied to estimate the Lomax distribution shape parameter.
  • Classical estimators (Maximum Likelihood, Ordinary Least Squares, etc.) and Bayesian estimators with various loss functions (Squared Error, Linear Exponential, Composite Linear Exponential) were used for comparison.
  • Monte Carlo simulations were conducted to assess performance using Mean Square Error (MSE).

Main Results:

  • Ridge Regression demonstrated promising results for estimating the Lomax distribution shape parameter.
  • The Ridge Regression method exhibited superior performance compared to the Ordinary Least Squares method.
  • Simulations indicated the potential applicability of Ridge Regression in real-world scenarios.

Conclusions:

  • Ridge Regression is a viable and effective method for estimating the Lomax distribution shape parameter.
  • The study highlights the advantages of Ridge Regression over traditional methods like Ordinary Least Squares in specific contexts.