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E-Bayesian and Bayesian Estimation for the Lomax Distribution under Weighted Composite LINEX Loss Function.

Afrah Al-Bossly1

  • 1Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.

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|December 21, 2021
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Summary
This summary is machine-generated.

This study introduces a novel weighted compound LINEX loss function (WCLLF) for estimating Lomax distribution shape parameters. Simulation results demonstrate that the WCLLF Bayesian and E-Bayesian estimators offer superior performance compared to existing methods.

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Area of Science:

  • Statistics
  • Probability Theory
  • Statistical Modeling

Background:

  • The Lomax distribution (LD) is widely used in reliability and survival analysis.
  • Accurate estimation of the LD shape parameter is crucial for model performance.
  • Existing loss functions may not optimally capture the asymmetric nature of parameter estimation errors.

Purpose of the Study:

  • To develop a new compound LINEX loss function (CLLF) for estimating the Lomax distribution shape parameter.
  • To introduce a weighted version (WCLLF) by incorporating weights into the CLLF.
  • To evaluate the performance of the WCLLF using Bayesian and expected Bayesian (E-Bayesian) estimation methods.

Main Methods:

  • Development of the compound LINEX loss function (CLLF) and its weighted variant (WCLLF).
  • Application of Bayesian and E-Bayesian estimation techniques using the WCLLF.
  • Performance evaluation through Monte Carlo simulations, comparing WCLLF estimators with Maximum Likelihood Estimation (MLE) and other loss functions.

Main Results:

  • The proposed WCLLF, when used with Bayesian and E-Bayesian estimators, demonstrated superior performance.
  • WCLLF-based estimators achieved the least mean averaged squared error in shape parameter estimation.
  • The study confirmed the effectiveness of the WCLLF over traditional loss functions like SELF and LLF.

Conclusions:

  • The weighted compound LINEX loss function (WCLLF) is a highly effective tool for estimating the Lomax distribution shape parameter.
  • Bayesian and E-Bayesian approaches utilizing WCLLF provide more accurate and reliable estimates.
  • This research offers an improved method for parameter estimation in statistical modeling involving the Lomax distribution.