Method of Moments Estimation of Usual Nutrient Intake Distributions

The parameters of the distribution of usual intakes of calcium, energy, iron, protein and vitamin C are estimated using four daily intakes of these dietary components for a sample of women selected in the Continuing Survey of Food Intakes by Individuals, conducted in 1985-86 by the Human Nutrition Information Service of the U.S. Department of Agriculture. The daily intakes for an individual are assumed to be the sum of the usual intake for that individual plus a measurement error. The variance and the third moment of the measurement errors for a given individual are assumed to be functions of the usual intake of that individual. For the five dietary components investigated, the standard deviation and cube root of the third moment of the measurement errors of an individual both appear to be linearly related to the usual intake for that individual. Moments of usual intake are estimated as functions of the sample moments of the four-day mean intakes and estimators for the parameters of the distribution of the measurement errors. Given estimates of the moments of usual intakes, the parameters of a particular distribution function can be estimated. The assumption that usual intakes of dietary components are distributed as Weibull random variables and that the measurement errors are generated as deviations of observations from the mean of Weibull distributions was accepted for all dietary components.