On Testing the Inverse Gaussian Distribution Hypothesis

The family of Inverse Gaussian (IG) distributions has applications in areas such as hydrology, lifetime testing, and reliability, among others. In this paper, a new characterization for this family of distributions is introduced and is used to propose a test of fit for the IG distribution hypothesis with unknown parameters. As a second test, observations are transformed to normal variables and then Shapiro-Wilk test is used to test for normality. Simulation results show that the proposed tests preserve the nominal test size and are competitive against some existing tests for the same problem. Three real datasets are used to illustrate the application of these tests.