ABSTRACT
This chapter focuses on methods based on the likelihood function. The asymptotic theory of maximum likelihood estimation on which the normal and chi-squared approximations are based does require the satisfaction of some 'regularity conditions' concerning the smoothness of the likelihood function. The fitted parameters are sensitive to the very short survival times. Estimation from censored samples when the number of failures is predetermined and the distribution exponential was considered by P. V. Sukhatme and B. Epstein and M. Sobel. D. J. Bartholomew derived asymptotic methods for the exponential distribution with fixed censoring times and also gave the exact distribution of the maximum likelihood estimator for Type I censoring. The computation and interpretation of standardized mortality ratios is discussed in most texts on medical statistics. The exponential and Weibull distributions are considered in more detail as illustrations of the general approach.
