Statistical inference based on left truncated and interval censored data from log-location-scale family of distributions

Abstract

Here, left truncated and interval censored data are analyzed by assuming that the underlying lifetime distribution belongs to log-location-scale family. In particular, lognormal and Weibull models are considered. Steps of stochastic expectation maximization (St-EM) algorithm are developed for the estimation of model parameters. MLEs are also obtained using Newton–Raphson method. Asymptotic confidence intervals for parameters are constructed using missing information principle, and parametric bootstrap approach. Through a simulation study, performances of proposed inferential methods are assessed. St-EM algorithm for point estimation and parametric bootstrap approach for constructing confidence intervals are recommended under this setup. Two datasets are analyzed for illustrative purpose. A prediction problem is also discussed.

Keywords:

• EM algorithm; Interval censoring; Left truncation; Lognormal distribution; Maximum likelihood estimates; missing information principle; Stochastic EM algorithm; Weibull distribution

Acknowledgments

The authors thank the associate editor and the anonymous reviewers for their constructive comments which have improved the representation of the material in this manuscript significantly.