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Classical and Bayesian Inference of Conditional Stress-Strength Model under Kumaraswamy Distribution
Fathy H Riad1,2, Mohammad Mehdi Saber3, Mehrdad Taghipour4
1Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia.
Computational Intelligence and Neuroscience
|August 10, 2021
Summary
This study introduces conditional stress-strength models for the Kumaraswamy distribution. Researchers derived the maximum likelihood estimator and its confidence intervals, alongside Bayesian and bootstrap estimations.
Area of Science:
- Statistics
- Probability Theory
- Reliability Engineering
Background:
- Stress-strength models are crucial for system reliability.
- Conditional stress-strength models offer a more nuanced analysis.
- The Kumaraswamy distribution is a flexible probability model.
Purpose of the Study:
- To extend stress-strength models to a conditional framework.
- To analyze the Kumaraswamy distribution within this conditional model.
- To provide statistical estimation and inference methods.
Main Methods:
- Maximum Likelihood Estimation (MLE) for model parameters.
- Asymptotic distribution theory for the MLE.
- Construction of confidence intervals.
- Bayesian estimation techniques.
- Bootstrap resampling methods.
Main Results:
- The maximum likelihood estimator for the conditional stress-strength model was derived.
- The asymptotic distribution of the estimator was determined.
- Confidence intervals for the estimator were established.
- Bayesian and bootstrap estimates were computed.
Conclusions:
- The study successfully developed and analyzed a conditional stress-strength model for the Kumaraswamy distribution.
- Various estimation techniques (MLE, Bayesian, bootstrap) were applied and evaluated.
- The findings contribute to reliability analysis and statistical modeling.
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