Simultaneous confidence intervals for mean differences of multiple zero-inflated gamma distributions with applications to precipitation

Abstract

Changes in precipitation over different periods or regions are important because they have significant effects on many aspects of everyday life. Comparison of multiple forms of precipitation between several periods or regions may therefore be helpful as an aid to decision-making. Precipitation data have generally been assumed to follow a gamma distribution. However, since some dry days have zero precipitation, a zero-inflated gamma distribution is more appropriate for fitting the data. In this article, we consider three fiducial methods (one accurate method and two approximate) to construct simultaneous confidence intervals for mean differences of multiple zero-inflated gamma distributions. Our simulation studies show that the exact method gives more accurate results than the two approximate ones, and it is applicable to various situations. However, the two approximate methods are much faster than the exact one. Also, they provide satisfactory results when the shape parameters are large. Real data on three-year daily precipitations for Waterloo in Canada are used to illustrate the three methods.