Fitting second-order finite mixture models to data with many censored values using maximum likelihood estimation

Finite mixture models, that is, weighted averages of parametric distributio ns, provide a powerful way to extend parametric families of distributions t o fit data sets not adequately fit by a single parametric distribution Firs t-order finite mixture models have been widely used in the physical, chemic al, biological, and social sciences for over 100 years. Using maximum likel ihood estimation, we demonstrate how a first-order finite mixture model can represent the large variability in data collected by the U.S. Environmenta l Protection Agency for the concentration of Radon 222 in drinking water su pplied from ground water, even when 25% of the data fall at or below the mi nimum reporting level. Extending the use of maximum likelihood, we also ill ustrate how a second-order finite mixture model can separate and represent both the variability and the uncertainty in the data set.