원문정보
초록
영어
This study seeks to focus on Bayesian and non-Bayesian estimation for the shape parameter of the Kumaraswamy distribution under type-II censored samples. Maximum likelihood estimation and Bayes estimation have been obtained using asymmetric loss functions. Posterior predictive distributions along with posterior predictive intervals have been derived under simple and mixture priors. Elicitation of hyper-parameter through prior predictive approach has also been discussed. As analytical comparison is difficult, so comparisons among these estimators have been made using Monte Carlo simulation study and some interesting comparisons have been presented. The findings of the study indicate that the Bayes estimation is superior to classical estimation under the suitable prior.
목차
1. Introduction
2. Classical Estimation
2.1. Maximum Likelihood Estimation
3. Loss Function
3.1. Degroot Loss Function (DLF)
3.2. Linex Loss Function (LLF)
3.3. General Entropy Loss Function (GELF)
4. Bayesian Analysis
4.1. The Posterior Distribution and Estimators under Inverse Levy Prior
4.2. The Posterior Distribution and Estimators under Gamma Prior
4.3. The Posterior Distribution and Estimators under Mixture of Gamma and Jeffreys Prior
5. Elicitation of Hyper-parameter
5.1. Method of Elicitation Through Prior Predictive Probabilities
5.2. Elicitation through Prior Predictive Probabilities Assuming Inverse Levy Prior
5.3. Elicitation through Prior Predictive Probabilities Assuming Gamma Prior
5.4. Elicitation Assuming Mixture of Gamma and Jeffreys Priors
6. Posterior Predictive Distributions
6.1. Posterior Distribution and Posterior Predictive Intervals Assuming Inverse Levy Prior
6.2. Posterior Distribution and Posterior Predictive Intervals Assuming Inverse Levy Prior
6.3. Posterior Distribution and Posterior Predictive Intervals Assuming Mixture of Gamma and Jeffreys Prior
7. Simulation Study
8. Conclusion
References