Normality transformations for environmental data from compound normal-lognormal distributions

The combination of lognormally distributed quantities of interest with normally distributed random measurement error produces data that follow a compound normal-lognormal (NLN) distribution. When the measurement error is large enough, such data do not approximate normality, even after a logarithmic transformation. This paper reports the results of a search for a transformation method for NLN data that is not only technically appropriate, but easy to implement as well. Three transformation families were found to work relatively well. These families are compared in terms of success in achieving normality and robustness, using simulated NLN data and actual environmental data believed to follow a NLN distribution. The exponential family of transformations was found to give the best overall results. This work was supported by the U.S. Department of Energy, Office of Environmental Restoration and Waste Management, under DOE Idaho Field Office Contract DE-AC07-76ID01570.