Construction of Optimal Unbiased Inference Procedures for the Parameters of the Gamma Distribution

Abstract

Methods for constructing uniformly most powerful unbiased two-sided tests of the parameters of the gamma distribution and the associated unbiased confidence intervals are discussed. These methods make use of existing results on construction of unbiased confidence intervals for the variance of a normal distribution. An approximation is derived for the conditional distribution of the statistic W _n = x/x given G _n = x/β. Tabulations which are convenient in calculating confidence limits for the shape parameter are given.

KEYWORDS:

• Gamma distribution
• Inference procedures
• Unbiased