Donald Richards, PhD

"Integral Transform Methods in Goodness-of-Fit Testing for Gamma Distributions"

Abstract: In recent years, integral transforms have been used widely in statistical inference, especially in goodness-of-fit 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. These distributions arise in many research areas, including queueing theory, neuroscience, reliability theory and life testing, and then is necessary to have goodness-of-fit tests for the underlying data. We prove that the null asymptotic distribution of the test statistic is a weighted sum of independent chi-square distributed random variables. We show further 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. Our analysis of the non-null asymptotic distribution also uncovers some unsolved problems in some series expansions related to work of Ramanujan and other mathematicians.

Dr. Richards is Professor of Statistics at Pennsylvania State University.