Statistical inference based on generalized Lindley record values

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.