Estimation of the standard deviation of a normal population from doubly censored samples using normal scores

SUMMARY Gupta's (1952) estimator of the standard deviation of a normal population, depending only on the expected values of the normal order statistics, is considered and further results showing its high efficiency relative to the best linear estimator for all forms of censoring are given. Tables which facilitate computation of the estimator, based on a sample of size n, are provided for 2 < n < 50 for complete samples and for 21 < n < 25 for censored samples, thereby extending tables which already exist for n < 20. Simple approximations for the variances of the estimators are also given.