An Estimation Procedure for the Contaminated Normal Distributions Arising in Clinical Chemistry

Mixtures of normal distributions have been used in modeling a wide variety of experimental data in fields as different as fisheries biology and medicine. A problem in the field of nutrition concerning estimation of the population proportion of anemic individuals from a sample of hemoglobin values has led to consideration of a class of mixtures of two components, where only the predominant component is assumed to be normal. The second component is assumed to contaminate only one side of the normal component (the side of contamination being known) but is of otherwise unspecified form. An estimation procedure is outlined for this problem. Monte Carlo methods are used to compare this procedure with the maximum likelihood (ML) method for mixtures of two normal components when the true model is (a) a Beta-normal mixture and (b) a normal-normal mixture. The new procedure compared favorably with the much-discussed ML method in certain situations not previously studied. Application of the two methods to real data gave remarkably similar results.

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