, Volume 36, Issue 1, pp 49-59

On approximate inference for the two-parameter gamma model

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Abstract

In applied work, the two-parameter gamma model gives useful representations of many physical situations. It has a two dimensional sufficient statistic for the two parameters which describe shape and scale. This makes it superficially comparable to the normal model, but accurate and simple statistical inference procedures for each parameter have not been available. In this paper, the saddlepoint approximation is applied to approximate observed levels of significance of the shape parameter. An averaging method is proposed to approximate observed levels of significance of the scale parameter. These methods are extended to the two-sample case.