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We apply the method of Hankel transforms to develop goodness-of-fit tests forgamma distributions with given shape parameter and unknown rate parameter,thereby extending results of Baringhaus and Taherizadeh (2010) on theexponential distributions. We derive the limiting null distribution of the teststatistic as an integrated squared Gaussian process, obtain the correspondingcovariance operator, and oscillation properties of its eigenfunctions. We showthat the eigenvalues of the operator satisfy an interlacing property, and weapply that property in approximating critical values of the test statistic inone of the two applications to data considered. Further, we establish theconsistency of the test. In studying properties of the test statistic under avariety of contiguous alternatives, we obtain the asymptotic distribution ofthe test statistic for gamma alternatives with varying rate or shape parametersand for a class of contaminated gamma models. We investigate the approximateBahadur slope of the test statistic under local alternatives and we establishthe validity of the Wieand condition, under which the approaches through theapproximate Bahadur efficiency and the Pitman efficiency are in accord.

Integral Transform Methods in Goodness-of-Fit Testing, I: The Gamma Distributions