Fiducial confidence limits and prediction limits for a gamma distribution: Censored and uncensored cases

The problems of finding confidence limits for the mean and an upper percentile, and upper prediction limits for the mean of a future sample from a gamma distribution are considered. Simple methods based on cube root transformation and fiducial approach are proposed for constructing confidence limits and prediction limits when samples are uncensored or censored. Monte Carlo simulation studies indicate that the methods are accurate for estimating the mean and percentile and for predicting the mean of a future sample as long as the percentage of nondetects is not too large. Algorithms for computing confidence limits and prediction limits are provided. Necessary R programs for calculating confidence limits and prediction limits are also provided as a supplementary file. The methods are illustrated using some real uncesnored/censored environmental data sets.