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Classical and Bayesian Inference Using Type-II Unified Progressive Hybrid Censored Samples for Pareto Model
M Nagy1, Adel Fahad Alrasheedi1
1Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.
Applied Bionics and Biomechanics
|May 9, 2022
Summary
This study introduces the Type-II unified progressive hybrid censored sample for reliability experiments. It applies this method to estimate Pareto distribution parameters using maximum likelihood and Bayesian approaches, demonstrating its practical applicability.
Area of Science:
- Statistics
- Reliability Engineering
- Survival Analysis
Background:
- Censored samples are crucial in lifetime and reliability experiments for cost and time efficiency.
- Traditional methods face challenges, leading to the development of advanced censored sample schemes.
- The Type-II unified progressive hybrid censored sample (T-II UPHCS) was recently proposed by Górny and Cramer (2018).
Purpose of the Study:
- To provide an overview of the Type-II unified progressive hybrid censored sample.
- To utilize T-II UPHCS for estimating unknown parameters of the Pareto distribution.
- To compare different estimation techniques, including maximum likelihood and Bayesian methods.
Main Methods:
- Application of Type-II unified progressive hybrid censored sampling.
- Computation of maximum likelihood estimates (MLEs) for Pareto distribution parameters.
- Derivation of Bayesian estimates under three distinct error loss functions.
- Development of one- and two-sample Bayesian predictive intervals.
- Conducting simulation studies for performance comparison.
- Analysis of real-world datasets to validate the model and methods.
Main Results:
- The study successfully applies T-II UPHCS to Pareto distribution parameter estimation.
- Both MLE and Bayesian approaches are investigated, offering a comprehensive analysis.
- Bayesian predictions (point and interval) are derived and presented.
- Simulation results provide insights into the comparative performance of different inference strategies.
- Real data analysis confirms the practical utility of the proposed censored sampling scheme and estimation techniques.
Conclusions:
- The Type-II unified progressive hybrid censored sample is a valuable tool for reliability studies.
- The presented estimation methods, particularly Bayesian approaches, offer robust parameter estimation and prediction for the Pareto distribution.
- The study validates the applicability and effectiveness of the T-II UPHCS in real-world scenarios.
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