Classical and Bayesian Inference for the Two-Parameter Rayleigh Distribution with Random Censored Data

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• The standard Rayleigh distribution has limitations in parameter estimation, especially with high minimum values in censored data.
• A single-parameter Rayleigh distribution lacks a threshold parameter crucial for many practical applications.

Purpose of the Study:

• To propose and evaluate a two-parameter Rayleigh distribution model for parameter estimation and reliability analysis under random censoring.
• To address the limitations of the conventional single-parameter Rayleigh distribution in handling threshold characteristics.

Main Methods:

• Development of a randomly censored data model.
• Derivation of classical inference methods, including maximum likelihood estimation (MLE).
• Construction of a Bayesian estimation framework and analysis of reliability characteristics.

Main Results:

• The two-parameter Rayleigh distribution demonstrates superior performance in parameter estimation and reliability analysis compared to the single-parameter model.
• Monte Carlo simulations confirm the effectiveness of the proposed estimators.
• Validation using real strength datasets confirms the model's practicality and superiority.

Conclusions:

• The two-parameter Rayleigh distribution provides a more accurate description of survival data with threshold characteristics.
• The proposed model offers improved model fit and reliability estimation for censored data.