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Statistical inference based on generalized Lindley record values.

Sukhdev Singh1, Sanku Dey2, Devendra Kumar3

  • 1Department of Mathematics, Chandigarh University, Punjab, India.

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Summary
This summary is machine-generated.

This study explores statistical estimation methods for the generalized Lindley distribution using lower record values. It compares frequentist and Bayesian approaches, offering insights into parameter estimation and prediction for reliability analysis.

Keywords:
62F1062F15Bayes estimatorGeneralized Lindley distributioninterval estimationlower record valuesmaximum likelihood estimatorprediction

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Area of Science:

  • Statistics
  • Probability Theory

Background:

  • Record values are crucial in reliability and survival analysis.
  • The generalized Lindley distribution is a flexible model for various data types.

Purpose of the Study:

  • To develop and compare frequentist and Bayesian estimation methods for generalized Lindley distribution parameters using lower record values.
  • To provide tools for parameter estimation and prediction in reliability engineering.

Main Methods:

  • Derivation of exact expressions for single and product moments of lower record values.
  • Application of maximum likelihood estimation (MLE) and Bayesian estimation with gamma priors.
  • Utilizing squared error and linear-exponential (LINEX) loss functions for Bayesian analysis.
  • Computation of Bayesian predictive estimates for future record values.

Main Results:

  • Exact formulas for moments of lower record values were derived.
  • Maximum likelihood estimators and asymptotic confidence intervals were obtained.
  • Bayes estimators and highest posterior density intervals were computed under different loss functions.
  • Monte Carlo simulations and a real data set analysis demonstrated the methods' performance.

Conclusions:

  • The study provides a comprehensive framework for estimating parameters and predicting future values of the generalized Lindley distribution based on lower record data.
  • Both frequentist and Bayesian methods offer valuable insights, with Bayesian approaches providing flexibility through different loss functions.