Publication Type

Journal Article

Version

Postprint

Publication Date

12-2011

Abstract

The mixed inverse Gaussian given by Whitmore (Scand. J. Statist., 13, 1986, 211–220) provides a convenient way for testing the goodness-of-fit of a pure inverse Gaussian distribution. The test is a one-sided score test with the null hypothesis being the pure inverse Gaussian (i.e. the mixing parameter is zero) and the alternative a mixture. We devise a simple score test and study its finite sample properties. Monte Carlo results show that it compares favourably with the smooth test of Ducharme (Test, 10, 2001, 271-290). In practical applications, when the pure inverse Gaussian distribution is rejected, one is interested in making inference about the general values of the mixing parameter. However, as it is well known that the inverse Gaussian mixture is a defective distribution; hence, the standard likelihood inference cannot be applied. We propose several alternatives and provide score tests for the mixing parameter. Finite sample properties of these tests are examined by Monte Carlo simulation.

Keywords

defective distribution, inverse gaussian, score tests

Discipline

Econometrics

Research Areas

Econometrics

Publication

Applied Stochastic Models in Business and Industry

Volume

27

Issue

6

First Page

633

Last Page

648

ISSN

1524-1904

Identifier

10.1002/asmb.876

Publisher

Wiley

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://dx.doi.org/10.1002/asmb.876

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Econometrics Commons

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