Model selection in radon data fusion

Fitting parametric models or the use of the empirical cumulative distribution function are problematic when it comes to the estimation of tail probabilities from small samples. A possible remedy is to fuse or combine the small samples with additional data from external sources and base the inference on the so called density ratio model with variable tilt functions, which widens the support of the estimated distribution of interest. This approach is illustrated using residential radon concentration data collected from western Pennsylvania.