A new characterization of the Gamma distribution and associated goodness-of-fit tests
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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. The result on the limit null distribution is used to prove the asymptotic validity of the parametric bootstrap that is implemented to run the tests. Further, we establish the global consistency of our tests in this bootstrap setting, and conduct a Monte Carlo simulation study to show the competitiveness to existing test procedures.
KeywordsBootstrap procedure Contiguous alternatives Density approach Gamma distribution Goodness-of-fit tests Stein’s method
The authors thank Norbert Henze for fruitful discussions and helpful comments on the presentation of the material. They also want to express their gratitude to an anonymous referee, an associate editor, and the journal editor, for their insights during the revision process, which led to a major improvement of the article.
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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
- Betsch S, Ebner B (2018) Testing normality via a distributional fixed point property in the Stein characterization. ArXiv e-prints arXiv:1803.07069
- Chen LHY, Goldstein L, Shao QM (2011) Normal approximation by Steins method. Springer, BerlinGoogle Scholar
- Husak GJ, Michaelsen J, Funk C (2007) Use of the gamma distribution to represent monthly rainfall in Africa for drought monitoring applications. Int J Climatol 27(7):935–944Google Scholar
- Plubin B, Siripanich P (2017) An alternative goodness-of-fit test for a gamma distribution based on the independence property. Chiang Mai J Sci 44(3):1180–1190Google Scholar
- R Development Core Team (2018) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar