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.
defective distribution, inverse gaussian, score tests
Applied Stochastic Models in Business and Industry
Desmond, A. F. and YANG, Zhenlin.
Score Tests for Inverse Gaussian Mixtures. (2011). Applied Stochastic Models in Business and Industry. 27, (6), 633-648. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/524
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