GOODNESS-OF-FIT TESTS FOR THE INVERSE GAUSSIAN DISTRIBUTION BASED ON THE EMPIRICAL LAPLACE TRANSFORM

NORBERT HENZE AND BERNHARD KLAR

Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr. 2, 76128 Karlsruhe, Germany

(Received July 17, 2000; revised February 19, 2001)

Abstract. 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.

Key words and phrases: Goodness–of–fit test, inverse Gaussian distribution, empirical Laplace transform, parametric bootstrap, smooth tests of fit.