Abstract
Due to the strikingly resemblance to the normal theory and inference methods, the inverse Gaussian (IG) distribution is commonly applied to model positive and right-skewed data. As the shape parameter in the IG distribution is greatly related to other important quantities such as the mean, skewness, kurtosis and the coefficient of variation, it plays an important role in distribution theory. This paper focuses on testing the equality of shape parameters in several inverse Gaussian distributions. Three tests are suggested: the exact generalized inference-based test, the asymptotic test and a test that is based on parametric bootstrap approximation. Simulation studies are undertaken to examine the performances of the these methods, and three real data examples are analyzed for illustration.
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Acknowledgments
The authors thank the editor and anonymous referees for their constructive comments and suggestions that lead to an improvement over an earlier version of this article. The research was supported by National Natural Science Foundation of China (No. 11071253), Beijing Nova Program (2010B066) and a grant from the Research Grants Council of Hong Kong.
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Niu, C., Guo, X., Xu, W. et al. Testing equality of shape parameters in several inverse Gaussian populations. Metrika 77, 795–809 (2014). https://doi.org/10.1007/s00184-013-0465-5
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DOI: https://doi.org/10.1007/s00184-013-0465-5