Fiducial inference on gamma distributions: two-sample problems with multiple detection limits

Abstract

The problems of finding confidence limits for the difference between two gamma means and the difference between two upper percentiles based on samples with multiple detection limits are considered. Simple methods for constructing confidence intervals and upper tolerance limits are developed based on cube root transformation and fiducial inferences. The performances of the proposed methods are evaluated by Monte Carlo simulations and are compared with parametric bootstrap and the method of variance estimates recovery. Computational results indicate that the proposed methods provide more satisfactory results even for small samples with high proportion of nondetects. The approaches are illustrated with some practical datasets.