COMMENTS: EM-BASED LIKELIHOOD INFERENCE FOR SOME LIFETIME DISTRIBUTIONS BASED ON LEFT TRUNCATED AND RIGHT CENSORED DATA AND ASSOCIATED MODEL DISCRIMINATION

摘要

The authors are to be commended for their comprehensive, thorough, and insightful investigation of the EM algorithm in estimating the parameters in lifetime distributions from data involving truncation and censoring. They develop detailed steps of the EM algorithm for several widely used distributions based on left truncated and right censored data. These distributions include the lognormal, Weibull, gamma, and generalized gamma distributions. The investigation on the generalized gamma distribution is of important practical value because it contains the exponential, gamma, Weibull and lognormal distributions as special cases, among others. Although the generalized gamma distribution has this nice property, its third parameter κ is usually challenging to estimate, even with censoring data only. Truncation can add a second layer of difficulty to the optimization of the log-likelihood function. The EM algorithm proposed in the paper can provide a more stable solution.