Statistical estimation of analytical data distributions and censored measurements

A numerical method was developed for estimating the shapes of unknown distributions of analytical data and for estimating the expected values of censored data points. The method is based conceptually on the normal probability plot. Data are ordered and then transformed by using a power function to achieve approximate linearity with respect to a computed normal cumulative probability scale. The exponent used in the power transformation is an index of the distribution shape, which covers a continuum on which normality is defined as d = 1 and log normality is defined as d = 0. Expected transformed values of censored points are computed from a straight line fitted to the transformed, accepted data, and these are then back-transformed to the original distribution. The method gives improved characterization of analytical data distributions, particularly in the distribution extremities. It also avoids the biases from improper handling of censored data arising from measurements near the analytical detection limit. Illustrative applications were computed for atmospheric SO2 data and for mineral concentrations in hamburgers.