Iterative maximum-likelihood estimation of the parameters of normal populations from singly and doubly censored samples

Iterative procedures are given for joint maximum-likelihood estimation based on singly and doubly censored samples from a normal population. The simultaneous equations yielding the maximum-likelihood estimates are obtained. Since their algebraic solution is impossible, iterative procedures are proposed which are applicable in the most general case in which both parameters are unknown and in special cases in which either of the parameters is known. The asymptotic variances and covariances are tabulated for 10% censoring intervals. A Monte Carlo investigation of the means and standard deviations of the maximum-likelihood estimators was made for 1000 samples from the standard normal population for n = 10 and n = 20. A comparison was then made of best linear unbiased estimators and maximum-likelihood estimators for n = 10 and n = 20.