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.
Keywords and phrases
Anderson-Darling test Characterizations Convolution Data transformations Gamma distribution Goodness-of-fit test Shapiro-Wilk test
The authors are grateful to the associate editor and two anonymous reviewers for their constructive comments and suggestions on the original version of this paper. The authors also thank Arturo Mancera-Rico for providing the dataset used in Example 2.
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