Fiducial-Based Statistical Intervals for Zero-Inflated Gamma Data

In practice, it is not uncommon to observe count data that possess excessive zeros (i.e., zero inflation) relative to the assumed discrete distribution. When data are semicontinuous, the log-normal and gamma distributions are often considered for modeling the positive part of the model. The problems of constructing a confidence interval for the mean and calculating upper prediction and tolerance limits of a zero-inflated gamma population are considered using generalized fiducial inference. Our simulation studies indicate that the proposed method is very satisfactory in terms of coverage properties and precision. The proposed intervals are calculated for lipid profiles from a study on non-small cell lung cancer.