Parameter inference for the inverse Weibull distribution under left-truncated and right-censored data: method comparison with an engineering reliability application

This paper develops and compares maximum likelihood, EM, and Bayesian inference methods for the two-parameter inverse Weibull distribution under left-truncated and right-censored data, with an application to insulating fluid breakdown time data.} Left-truncated and right-censored data commonly arise in engineering applications and life-testing studies, and ignoring the underlying observation mechanism may lead to biased parameter inference. Since the inverse Weibull distribution has been widely used in reliability engineering, this paper investigates inference for the two-parameter inverse Weibull distribution under left-truncated and right-censored data. Maximum likelihood estimation, the EM algorithm, and Bayesian estimation are developed, together with the corresponding interval estimation procedures. Monte Carlo simulation results show that, as the sample size increases, the RMSE and interval lengths of the three methods generally decrease, while the coverage probabilities remain close to the nominal level. The Bayesian method performs more stably in small-sample settings or under heavier truncation and censoring, whereas maximum likelihood estimation is more computationally efficient when sufficient sample information is available. Finally, a real engineering dataset is used to illustrate the effectiveness of the proposed methods.