Bayesian Inference for the Kumaraswamy Distribution under Generalized Progressive Hybrid Censoring

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• Incomplete data and censoring are common challenges in survival analysis and life testing.
• The Kumaraswamy distribution is increasingly used for modeling various phenomena.
• Generalized progressive hybrid censoring schemes offer flexibility in data collection.

Purpose of the Study:

• To estimate unknown parameters of the Kumaraswamy distribution under a generalized progressive hybrid censoring scheme.
• To estimate reliability using both maximum likelihood and Bayesian approaches.
• To compare the performance of different estimation methods through simulation.

Main Methods:

• Derivation of Maximum Likelihood Estimators (MLEs).
• Development of Bayesian estimators using symmetric and asymmetric loss functions (squared error, general entropy, linex).
• Application of Lindley approximation and Tierney and Kadane method for Bayesian computations.

Main Results:

• The study successfully derives both MLEs and Bayesian estimators for the Kumaraswamy distribution parameters and reliability.
• Simulation results provide a comparative analysis of the proposed estimators' efficiency.
• The methods are illustrated using a practical, real-life example.

Conclusions:

• The proposed estimation techniques are effective for analyzing data from Kumaraswamy distribution under the specified censoring scheme.
• The comparison aids in selecting appropriate estimators based on desired statistical properties.
• This research contributes to the robust analysis of censored survival data.