Likelihood analysis and stochastic EM algorithm for left truncated right censored data and associated model selection from the Lehmann family of life distributions

Abstract

The Lehmann family of distributions includes Weibull, Gompertz, and Lomax models as special cases, all of which are quite useful for modeling lifetime data. Analyses of left truncated right censored data from the Lehmann family of distributions are carried out in this article. In particular, the special cases of Weibull, Gompertz, and Lomax distributions are considered. Maximum likelihood estimates of the model parameters are obtained. The steps of the stochastic expectation maximization algorithm are developed in this context. Asymptotic confidence intervals for the model parameters are constructed using the missing information principle and two parametric bootstrap approaches. Through extensive Monte Carlo simulations, performances of the inferential methods are examined. The effect of model misspecification is also assessed within this family of distributions through simulations. As it is quite important to select a suitable model for a given data, a study of model selection based on left truncated right censored data is carried out through extensive Monte Carlo simulations. Two examples based on real datasets are provided for illustrating the models and methods of inference discussed here.