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Goodness-of-fit tests for the inverse Gaussian distribution based on the empirical Laplace transform. (English) Zbl 1012.62047

Summary: This paper considers two flexible classes of omnibus goodness-of-fit tests for the inverse Gaussian distribution. The test statistics are weighted integrals over the squared modulus of some measure of deviation of the empirical distribution of given data from the family of inverse Gaussian laws, expressed by means of the empirical Laplace transform. Both classes of statistics are connected to the first nonzero component of Neyman’s smooth test for the inverse Gaussian distribution. The tests, when implemented via the parametric bootstrap, maintain a nominal level of significance very closely. A large-scale simulation study shows that the new tests compare favorably with classical goodness-of-fit tests for the inverse Gaussian distribution, based on the empirical distribution function.

MSC:

62G10 Nonparametric hypothesis testing
62F40 Bootstrap, jackknife and other resampling methods
62E20 Asymptotic distribution theory in statistics
62F03 Parametric hypothesis testing
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