Left truncated and right censored Weibull data and likelihood inference with an illustration

The Weibull distribution is a very popular distribution for modeling lifetime data. Left truncation and right censoring are often observed in lifetime data. Here, the EM algorithm is applied to estimate the model parameters of the Weibull distribution fitted to data containing left truncation and right censoring. The maximization part of the EM algorithm is carried out using the EM gradient algorithm (Lange, 1995). The Weibull distribution is also fitted using the Newton–Raphson (NR) method. The two methods of estimation are then compared through an extensive Monte Carlo simulation study. The asymptotic variance–covariance matrix of the MLEs under the EM framework is obtained through the missing information principle (Louis, 1982), and asymptotic confidence intervals for the parameters are then constructed. The asymptotic confidence intervals corresponding to the missing information principle and the observed information matrix are compared in terms of coverage probabilities, through a simulation study. Finally, all the methods of inference discussed here are illustrated through some numerical examples.