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Point estimation and related classification problems for several Lindley populations with application using COVID-19

Debasmita Bal1, Manas Ranjan Tripathy1, Somesh Kumar2

  • 1Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India.

Journal of Applied Statistics
|July 29, 2024
PubMed
Summary

This study introduces improved Bayes estimators for the Lindley distribution using Markov chain Monte Carlo (MCMC) and Tierney and Kadane

Keywords:
62F1062F1262F1562H30Approximate Bayes estimatorBayesian plug-in classification ruleLindley's approximationMarkov chain Monte Carlo (MCMC) methodTierney and Kadane's approximationlikelihood accordance classifierprobability of misclassification

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Area of Science:

  • Statistical modeling
  • Bayesian inference
  • Machine learning

Background:

  • The Lindley distribution is a flexible model for various data types.
  • Accurate parameter estimation and classification are crucial in statistical analysis.

Purpose of the Study:

  • To develop and evaluate novel Bayes estimators for the Lindley distribution parameter.
  • To propose and assess classification rules based on these estimators.
  • To apply the methods to real-world COVID-19 data.

Main Methods:

  • Derivation of Bayes estimators using Markov chain Monte Carlo (MCMC) and Tierney and Kadane's methods.
  • Convergence analysis of Bayes estimators to the Maximum Likelihood Estimator (MLE).
  • Numerical comparison of estimators using bias and Mean Squared Error (MSE).
  • Development of classification rules, including a likelihood accordance function rule.
  • Evaluation of classification rules using Expected Probability of Misclassification (EPM).

Main Results:

  • Proposed Bayes estimators demonstrate superior performance compared to existing methods in simulation studies.
  • Bayes estimators converge to the MLE as sample size increases.
  • Classification rules show effective performance in numerical evaluations.

Conclusions:

  • The developed Bayes estimators and classification rules offer improved accuracy for Lindley distributed data.
  • The methodology is applicable to real-world problems, such as analyzing COVID-19 data.