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A new characterization of the Gamma distribution and associated goodness of fit tests (1806.06028v2)
Published 15 Jun 2018 in stat.ME, math.ST, and stat.TH
Abstract: We propose a class of weighted $L_2$-type tests of fit to the Gamma distribution. Our novel procedure is based on a fixed point property of a new transformation connected to a Steinian characterization of the family of Gamma distributions. We derive the weak limits of the statistic under the null hypothesis and under contiguous alternatives. Further, we establish the global consistency of the tests and apply a parametric bootstrap technique in a Monte Carlo simulation study to show the competitiveness to existing procedures.