Modified goodness-of-fit tests for the inverse Gaussian distribution. (English) Zbl 0900.62231

Summary: Modified Kolmogorov–Smirnov (KS), Kuiper (V), Cramer–von Mises (CV), Watson (W), Anderson–Darling (AD) and sequential goodness-of-fit tests are developed for the inverse Gaussian distribution with unknown parameters. A Monte Carlo procedure is employed to generate critical values for a wide range of sample sizes and shape parameters. Power studies indicate that the W test is most effective against alternate distributions that are very similar in shape to the null inverse Gaussian distribution. Otherwise, the modified AD test generally demonstrates the highest power among single tests. To eliminate the need for extensive critical value tables, functional relationships between critical values, sample sizes, and shape parameters are reported.


62G10 Nonparametric hypothesis testing
65C99 Probabilistic methods, stochastic differential equations
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