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

This study focuses on parameter estimation and reliability analysis for the two-parameter Rayleigh distribution under random censoring. It is shown that directly fitting the standard Rayleigh distribution can lead to substantial estimation errors, especially when the dataset contains a markedly high minimum value. To overcome the limitation of the conventional single-parameter Rayleigh distribution, which lacks a threshold parameter in practical applications, a two-parameter Rayleigh distribution model is proposed. The main research contents include the following: establishing a randomly censored data model; deriving classical inference methods based on maximum likelihood estimation along with several other classical estimation techniques; and constructing a Bayesian estimation framework. We also analyze several reliability and experimental characteristics by deriving their corresponding estimates. A Monte Carlo simulation study is carried out to assess the performance of the proposed estimators. Finally, the practicality and superiority of the two-parameter model are validated using real strength datasets. The results demonstrate that the two-parameter Rayleigh distribution can more accurately describe survival data with threshold characteristics and outperforms the single-parameter model in terms of model fit and reliability estimation.