Estimating the mean and standard deviation from a censored normal sample

Abstract

SUMMARY The relation g(x) -c- + fx, where g(x) is the ratio of the ordinate and the probability integral of a normal distribution, is used to derive estimators ,uc and oc of the population mean and standard deviation, from a censored normal sample. These estimators are easy to compute. For symmetrical censoring ,uc is unbiased and for moderate censoring the bias in both ,c and oc is small. In terms of efficiency, ,c and o-c seem to be as good as the maximum likelihood (M.L.) estimators and better than the best linear unbiased (B.L.U.) estimators. A pair of nearly unbiased estimators ,u and o-, more efficient than the B.L.U. estimators, is also obtained.