Classical and Bayesian Estimation of the Two-Parameter Maxwell Distribution Under Random Censoring

This paper investigates the problem of parameter estimation and reliability analysis for the two-parameter Maxwell distribution under a random censoring mechanism. To address the limitation of the traditional single-parameter Maxwell distribution in practical applications, which lacks the threshold parameter, this paper proposes a two-parameter Maxwell distribution model. By introducing a threshold parameter, this model can more accurately characterize survival data with a minimum life or guaranteed operating time. Specifically, we construct a random censoring data model wherein both the failure time and censoring time are assumed to follow a two-parameter Maxwell distribution. The main research contents include: establishing a randomly censored data model, deriving classical inference methods based on maximum likelihood estimation. Under the general entropy loss function, Bayesian estimation is conducted using conjugate inverse Gamma priors for scale parameters and a uniform prior for the threshold parameter. A hybrid MCMC algorithm is implemented to generate posterior samples and construct highest posterior density credible intervals. We compare their performance through Monte Carlo simulations, evaluating finite-sample behavior in terms of bias, mean squared error, and interval estimation, and finally validating the practicality and superiority of the two-parameter model using real medical datasets from a colon cancer clinical trial. The results demonstrate that the two-parameter Maxwell distribution can more accurately describe survival data with threshold characteristics and outperforms the single-parameter model in terms of model fit and reliability estimation.