A comparison of three methods of fitting the normal ogive

The Mueller-Urban method of fitting the normal ogive is derived, and the inadequacies of its inherent assumptions are discussed. This and the unweighted least squares method are compared to the maximum likelihood solution which is shown to be very close to the ideal least squares solution. As an empirical demonstration of the superiority of the maximum likelihood solution, random ogives are fitted by all three methods and they are compared on the basis of the expected values and the standard errors of the estimates. It is concluded that the maximum likelihood solution is uniformly superior to the others in all respects.This research was done under Contract Nonr-248(55) between the Office of Naval Research and The Johns Hopkins University. This is Report No. 18 under that contract. Reproduction in whole or in part is permitted for any purpose of the United States Government. This paper is part of a dissertation submitted to The Johns Hopkins University. Part of this work was done while the author was a National Institutes of Health Research Fellow.Now at The Biometric Laboratory, The George Washington University. The author is indebted to Dr. Wendell R. Garner for his valuable advice and encouragement, and to Jerome Cornfield for several helpful discussions.