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Statistical Inference of the Generalized Inverted Exponential Distribution under Joint Progressively Type-II
1School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China.
Entropy (Basel, Switzerland)
|May 28, 2022
Summary
This study introduces statistical inference for the generalized inverted exponential distribution using joint progressively censored data. Methods include maximum likelihood estimates and Bayesian inference for parameter estimation and interval calculations.
Area of Science:
- Statistics
- Probability Theory
Background:
- The generalized inverted exponential distribution is a flexible model for reliability and survival analysis.
- Progressive censoring is an efficient data collection method in life-testing experiments.
Purpose of the Study:
- To develop statistical inference methods for the generalized inverted exponential distribution under joint progressive type-II censoring.
- To compare different estimation techniques, including maximum likelihood and Bayesian approaches.
Main Methods:
- Application of the Expectation-Maximization (EM) algorithm for Maximum Likelihood Estimates (MLEs).
- Utilizing the missing value principle to derive the observed information matrix.
- Employing bootstrap methods for interval estimations.
- Implementing Bayesian inference with informative and non-informative priors.
- Using importance sampling for Bayesian estimates and credible intervals under various loss functions.
- Considering parameter order restrictions.
Main Results:
- The study provides a comprehensive framework for parameter estimation and confidence/credible interval construction.
- It demonstrates the utility of the EM algorithm and Bayesian methods for this distribution and censoring scheme.
- Performance evaluation through Monte Carlo simulations and real data analysis.
Conclusions:
- The proposed methods offer robust statistical inference for the generalized inverted exponential distribution with joint progressively censored data.
- The study highlights the effectiveness of both frequentist and Bayesian approaches, especially when dealing with order restrictions.
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