Abstract:
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In recent years, integral transforms have been used widely in statistical inference, especially in goodness-of-fit testing. Gamma distributions with known shape parameters are frequently used as models in many research areas, such as queueing theory, neuroscience, reliability theory, and life testing. In this talk, we apply Hankel transform theory to propose an integral-type test statistic for goodness-of-fit tests for gamma distributions with known shape parameters. We prove that the null asymptotic distribution of the test statistic is a weighted sum of independent chi-square distributed random variables. Further, we show that the proposed test is consistent against each fixed alternative distribution, and we derive the non-null asymptotic distribution of the test statistic under a sequence of contiguous alternatives.
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