Simple and accurate inference for the mean of the gamma model

The two-parameter gamma model is widely used in reliability, environmental, medical and other areas of statistics. It has a two-dimensional sufficient statistic, and a two-dimensional parameter which can be taken to describe shape and mean. This makes it closely comparable to the normal model, but it differs substantially in that the exact distribution for the minimal sufficient statistic is not available. Some recently developed asymptotic theory is used to derive an approximation for observed levels of significance and confidence intervals for the mean parameter of the model. The approximation is as easy to apply as first-order methods, and substantially more accurate.