Confidence intervals for zero-inflated gamma distribution

Abstract

The problems of constructing confidence intervals (CIs) for the mean of a gamma distribution containing zero values are considered. Three different methods for constructing such CIs based on Parametric Bootstrap (PB) method, fiducial inference and the method of variance of estimates recovery (MOVER) are developed. The performances of the proposed CIs are evaluated by Monte Carlo simulation and compared with a published method, asymptotic normal (AN) method. The simulation studies indicate that the proposed methods perform better than the existing method (AN) according to coverage probabilities (CPs), tail error rates, robustness and time comparison. All the methods are illustrated using a dataset for HIV risk behavior in adolescent girls and a dataset for the immunologic response to combination therapy for HIV children. Recommendations are made at the end of the articles.