EM-based likelihood inference for some lifetime distributions based on left truncated and right censored data and associated model discrimination.

*(English)*Zbl 1397.62365Summary: Data arising from life-testing and reliability studies are often left truncated and right censored. Some of the most commonly used distributions to model lifetime data are the lognormal, Weibull, gamma and exponential distributions. Here, the EM algorithm is used to estimate the parameters of the lognormal, Weibull and gamma models based on left truncated and right censored data. The parsimonious model that includes the lognormal, Weibull, exponential and gamma distributions as special cases is the generalized gamma distribution. The EM algorithm steps for the generalized gamma distribution are also derived based on left truncated and right censored data. The asymptotic variance-covariance matrices of the MLEs are derived by using the missing information principle T. A. Louis [J. R. Stat. Soc., Ser. B 44, 226–233 (1982; Zbl 0488.62018)], and then the asymptotic confidence intervals for the parameters are obtained. The Newton-Raphson method is also applied to obtain the MLEs for the lognormal, Weibull and gamma distributions, for comparison purpose. The methods of inference are compared through extensive Monte Carlo simulation studies, and some numerical examples are given to illustrate all the methods of inference developed here. A model discrimination problem is addressed using the information-based criteria.

##### MSC:

62N01 | Censored data models |

62N02 | Estimation in survival analysis and censored data |

62N05 | Reliability and life testing |