Goodness of fit for the inverse Gaussian distribution. (English) Zbl 0765.62051

Summary: For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution-function statistic \(A^ 2\) is studied. Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated, and in the second the distribution function is estimated by its Rao-Blackwell distribution estimator.
A table is given for the asymptotic critical points of \(A^ 2\). These are shown to depend only on the ratio of the unknown parameters. An analysis is provided of the effect of estimating the ratio to enter the table for \(A^ 2\). This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.


62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
62Q05 Statistical tables
62G20 Asymptotic properties of nonparametric inference
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