Hindawi Publishing Corporation Advances in Decision Sciences Volume 2012, Article ID 150303, 9 pages doi:10.1155/2012/150303 Research Article Comparison of Some Tests of Fit for the Inverse Gaussian Distribution D. J. Best, 1 J. C. W. Rayner, 1, 2 and O. Thas 2, 3 1 School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia 2 Centre for Statistical and Survey Methodology, School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia 3 Department of Mathematical Modelling, Statistics and Bioinformatics, 9000 Gent, Belgium Correspondence should be addressed to J. C. W. Rayner, john.rayner@newcastle.edu.au Received 27 April 2012; Revised 18 July 2012; Accepted 26 July 2012 Academic Editor: Shelton Peiris Copyright q 2012 D. J. Best et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper gives an empirical investigation of some tests of goodness of fit for the inverse Gaussian distribution. 1. Introduction The inverse Gaussian IG distribution is an important statistical model for the analysis of positive data. See, for example, Seshadri 1. In its standard form the distribution, denoted IGλ, μ, depends on the shape parameter λ> 0 and the mean μ> 0. Its probability density function is √ λ √ 2πx 3 exp  - λ ( x - μ ) 2 2μ 2 x  , for x> 0, and zero otherwise. 1.1 Let X 1 ,X 2 ,...,X n be a sequence of independent observations. We wish to test H 0 : X is distributed as IGλ, μ for λ> 0 and μ> 0 against H A and not H 0 . The maximum likelihood estimators are  λ  ⎧ ⎨ ⎩ ∑ n i1  1/X i - 1/ X  n ⎫ ⎬ ⎭ -1 ,  μ  X. 1.2 Put  ϕ   λ/  μ.