This paper applies maximum likelihood estimation techniques to determine suitable models for dietary intake distributions. Hypothesis test results indicate that while the gamma and Weibull models appear suitable for describing the intake distributions of some dietary components, a more flexible family of distributions is required in order to appropriately encompass all dietary component distributions.
Six nutrients are considered in the analysis including calcium, energy, iron, protein, vitamin A, and vitamin C. Based on chi-square goodness-of-fit tests, we conclude that the three parameter, generalized gamma family of distributions accurately describes the distributions of all six dietary components.
The additional flexibility of this family results in large standard errors for the parameter estimates. However, the standard errors of the estimated percentage of the population below a specified level of nutrient intake appear precise and allow for substantive conclusions regarding nutritional inadequacy to be made.
Helterbrand, Jeffrey D., "Maximum Likelihood Estimation of Dietary Intake Distributions" (1992). CARD Working Papers. 139.