A comparative study of lognormal, gamma and beta modelling in radon mapping with recommendations regarding bias, sample sizes and the treatment of outliers.

Radon risk maps have been produced in many countries using non-geologically based techniques utilising the lognormal and gamma distributions to display point estimates of the probability, P(RL), that indoor radon levels will exceed a reference level. Recent work on updating radon maps in Ireland prompted an examination of various statistical issues associated with non-geologically based radon mapping techniques. The purpose of this paper is to compare existing techniques with a new theoretically unbiased model which uses the beta distribution to estimate P(RL). We examine this new beta based model and four existing models for bias using simulated test data sets. Producing confidence intervals for P(RL), we also analyse the relationship between sample size and estimation error for each model and finally we consider the effect of extreme values on estimation procedures. We demonstrate that, under the assumption of lognormally distributed data with outliers, a two stage approach to testing which first detects and removes outliers from the data and then applies the beta based method is most satisfactory from both a theoretical and empirical perspective.