Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 362--374

A GOODNESS-OF-FIT TEST FOR THE INVERSE GAUSSIAN DISTRIBUTION USING ITS INDEPENDENCE CHARACTERIZATION

By

GOVIND S. MUDHOLKAR, University of Rochester
RAJESHWARI NATARAJAN, Southern Methodist University

and

YOGENDRA P. CHAUBEY, Concordia University

SUMMARY. The class of inverse Gaussian (IG) distributions share substantial analytical elegance with the class of normal distributions, and they are widely used as models in many diverse areas of applied research. It is well-known that independence of the sample mean and sample variance characterizes a normal population. This was used by Lin and Mudholkar (1980), see also Mudholkar et al. (1996), for developing tests of normality. An analogous property, namely independence of the maximum likelihood estimates of the two parameters, characterizes the inverse Gaussian distribution. In this paper we use this characterization to develop the analogous goodness-of-fit test for the inverse Gaussian model. Monte Carlo methods are used in the construction and evaluation of the test.

AMS (1991) subject classification. Primary: 62F03, secondary 62E17, 62E20, 62E25.

Key words and phrases. Goodness-of-fit, independence characterization, inverse Gaussian distribution.

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