Parametric and semi-nonparametric model strategies for the estimation of distributions of chemical contaminant data

Abstract

The determination of an appropriate distribution for concentration data is of major importance in chemical risk assessment. The selection and the estimation of an appropriate distribution is hindered by observations below the limit-of-detection and the limit-of-quantification, leading to left-censored and interval-censored data. The log-normal distribution is a typical choice, owing its popularity from the use of the log transform in daily laboratory practice, in combination with the nice mathematical and computational properties of the normal distribution. But the log-normal should not be the only choice and other distributions need to be considered as well. Here we focus on several families of distributions that are related to the log-normal distribution in some direct or indirect way, and that are parametric or semi-nonparametric extensions of the log-normal distribution: the log-skew-normal, the log-t, the log-skew-t, the Weibull, the gamma, the generalized-gamma, and the semi-nonparametric estimator of Zhang and Davidian (Biometrics 64(2):567–669, 2008). Whereas Nysen et al. (Stat Med 31:2374–2385, 2012) developed methodology to test the goodness-of-fit of a particular hypothesized distribution, our interest here goes to model selection and model averaging, using all parametric models only or in addition the series of extensions of the log-normal underlying the semi-nonparametric estimator. The models and methods of selection and averaging are further investigated through simulations and illustrated on data of cadmium concentration in food products.