Goodness of fit for the inverse Gaussian distribution

Abstract

For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution‐function statistic A2 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 A2. 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 A2. This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.

Cumulant plots and goodness-of-fit tests for the inverse Gaussian distribution

“…Folks and Chhikara [24] found that the fit of the IG2 to this data is not satisfactory. The same conclusion may be drawn from O'Reilly and Rueda [11] who found a p-value of 0.04 by using a Monte Carlo approximation of the distribution of the AD test statistic with the parameters replaced by their ml estimates. The modified AD test of Pavur et al [9] barely accepts the IG2 model (test statistic = 8.273, 95% interpolated critical value = 8.2885, p-value=slightly over 5%).…”

“…We also find non-significant results at the 5% level with the modified KS (test statistic = 0.176) and AD tests (test statistic = 6.552, p-value between 10% and 20%) of Edgeman et al [8] and Pavur et al [9] and with the T 2 test (p − value = 0.372) of Natarajan and Mudholkar [16]. On the contrary, O'Reilly and Rueda [11] rejected the IG2 hypothesis at the 5% level based on the asymptotic distribution of the AD test statistic (p-value < 0.025) and Gunes et al [10] concluded similarly with their modified WA test. Also, the IG2 can be rejected at the 5% level by the independence Z-test of Mudholkar et al [14] (p-value = 0.037) and by the entropy test of Mudholkar and Tian [15] (K mn = 2.675 found for m = 3, p-value ∼ = 0.05).…”

“…Separate formulas were found for five levels of significance which involve the sample size and the estimated φ. On the other hand, O'Reilly and Rueda [11] found approximate critical points of the asymptotic null distribution of the AD test statistic. Two procedures are proposed for finding the test statistic with the first relying on the ml estimates of the parameters and the second on the Rao-Blackwell distribution estimator of the IG2 distribution function.…”

“…The authors show that both procedures yield the same asymptotic null distribution. Exact edf tests for the IG2 were proposed by Nguyen and Dinh [12] but Gracia-Medrano and O'Reilly [13] showed that they have inferior power performance in small samples as compared with the tests of Edgeman et al [8] and O'Reilly and Rueda [11].…”

A regression characterization of inverse Gaussian distributionsand application to EDF goodness‐of‐fit tests

“…In their study, at some alternative distributions, and with reasonable, not large, sample sizes, the exact EDF goodness-of-fit tests based on this transformation behave pretty well comparing with the other approximate EDF goodness-of-fit tests. The other goodness-of-fit tests for inverse Gaussian distributions using EDF statistics were given by Edgeman et al [3], O'Reilly and Rueda [6], and Pavur et al [7]. For detailed references, see Seshadri [10].…”