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Optimal sampling and statistical inferences for Kumaraswamy distribution under progressive Type-II censoring schemes
Osama E Abo-Kasem1, Ahmed R El Saeed2, Amira I El Sayed3
1Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, Egypt.
Scientific Reports
|July 26, 2023
Summary
This study introduces new methods for estimating parameters of the Kumaraswamy distribution using progressive Type-II censoring. It compares Bayesian and non-Bayesian approaches, offering insights for reliability analysis.
Area of Science:
- Statistics
- Probability Theory
- Reliability Engineering
Background:
- The Kumaraswamy distribution is widely used in various fields.
- Progressive Type-II censoring is an efficient data collection method.
- Parameter estimation for this distribution under censoring is crucial for accurate analysis.
Purpose of the Study:
- To develop and compare non-Bayesian and Bayesian estimation techniques for the Kumaraswamy distribution parameters.
- To investigate the performance of different estimators and censoring schemes.
- To provide practical guidance through real data application.
Main Methods:
- Maximum Likelihood Estimation (MLE) and Maximum Product Spacings (MPS).
- Bayesian estimation using Squared Error, Linear Exponential, and General Entropy loss functions.
- Lindley approximation and Markov Chain Monte Carlo (MCMC) for Bayesian estimates.
- Derivation of asymptotic distributions and confidence/credible intervals.
- Optimization of progressive censoring schemes.
Main Results:
- Derivation of MLE and MPS estimators for Kumaraswamy parameters.
- Obtained Bayesian estimators and highest posterior density credible intervals.
- Evaluation of estimator performance through simulation studies.
- Identification of optimal progressive censoring schemes.
Conclusions:
- The study provides a comprehensive framework for parameter estimation of the Kumaraswamy distribution under progressive Type-II censoring.
- Both Bayesian and non-Bayesian methods offer valuable estimation techniques.
- The findings are illustrated with a real-world data application, demonstrating practical utility.
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