This paper considers the statistical inferences of inverse Weibull distribution under progressive type-Ⅱ censored sample, which is a common distribution in reliability analysis. Two commonly used parameter estimation methods, maximum likelihood estimation and Bayesian estimation, are used in this paper, along with the inverse moment estimation. First, we derive the maximum likelihood estimators of parameters and propose Newtown-Raphson iteration method to solve these estimators. Assuming that shape and rate parameters are independent and follow gamma priors, we further obtain the Bayesian estimators by Lindley approximation. We also derive the inverse moment estimators and construct the generalized confidence intervals using the generalized pivotal quantity. To compare the estimation effects of these methods, we implement Monte Carlo simulation with the help of MATLAB. The simulation results show that the Bayesian estimation method outperforms the other two methods in terms of mean squared error. Finally, we verify the feasibility of these methods by analyzing a set of real data. The results indicate that the Bayesian estimation method provides more accurate estimates than the other two methods.

A two-parameter generalized Lindley distribution is proposed, whose probability density function contains two models that are particularly well-suited for lifetime studies: the inverted J-type and the unimodal left-leaning type. Some of the main numerical characteristics of the proposed distribution were investigated. Additionally, based on progressively type-Ⅱ censored samples, three estimation methods were used to estimate the parameters, reliability function, and hazard function of the distribution: maximum product spacing estimation, maximum likelihood estimation, and Bayesian estimation. Bayesian estimators were obtained under squared error and general entropy loss functions, and the Metropolis-Hastings algorithm was used to obtain Bayesian estimates. In addition to point estimation, corresponding asymptotic confidence intervals and the highest posterior density intervals were also studied. Through Monte Carlo simulation, we measured the performance of the three estimators using four criteria. Finally, the ability of the proposed distribution to accurately fit the data was demonstrated using a real dataset.