Using the EM algorithm for inference in a mixture of distributions with censored but partially identifiable data

This paper describes an implementation of the EM algorithm for the statistical analysis of a finite mixture of distributions arising when data are censored but partially identifiable. We consider a scheme of type I censoring where censoring times are random. The estimation of standard errors proposed by Meng and Rubin (1991. Using EM to obtain asymptotic variance–covariance matrices: the SEM algorithm. J. Amer. Statist. Assoc. 86(416), 899–909) is also implemented in the context of the above mixture. A Bayesian method introduced in Contreras-Cristán et al. (2003. Statistical inference for mixtures of distributions for censored data with partial identification. Commun. in Statist. Theory Methods 32(4), 749–774) for the case of a constant censoring value is extended to the case of random censoring times. Comparisons with different methods are carried out both with simulated data and with the observations on failure times for communication transmitter–receivers of Mendenhall and Hader (1958. Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data. Biometrika 45, 504–520).