References
- Chhikara , R. S. ( 1975 ). Optimum tests for comparison of two inverse Gaussian distribution means . Austral. J. Statist. 17 ( 2 ): 77 – 38 .
- Chhikara , R. S. , Folks , J. L. ( 1976 ). Optimum test procedures for the mean of first passage time in Brownian motion with positive drift (inverse Gaussian distribution) . Technometrics 18 : 189 – 93 .
- Das Gupta , S. , Anderson , T. W. , Mudholkar , G. S. ( 1964 ). Monotonicity of the power functions of some tests of the multivariate linear hypothesis . Ann. Mathemat. Statist. 35 : 200 – 205 .
- Jones , M. C. ( 2008 ). On reciprocal symmetry . J. Statist. Plann. Infer. 138 ( 10 ): 3039 – 3043 .
- Kendall , M. G. , Stuart , A. ( 1979 ). The Advanced Theory of Statistics, 2, Inference and Relationship. , 4th ed. London : Griffin .
- Marcus , M. , Minc , H. ( 1964 ). Survey of Matrix Theory and Matrix Inequalities . Boston : Allyn and Bacon Inc .
- Miura , C. K. ( 1978 ). Tests for the mean of the inverse Gaussian distribution . Scand. J. Statist. 5 : 200 – 204 .
- Mudholkar , G. S. ( 1965 ). A class of tests with monotone power functions for two problems in multivariate statistical analysis . Ann. Mathemat. Statist. 36 : 1794 – 1801 .
- Mudholkar , G. S. ( 1966 ). The integral of an invariant unimodal function over an invariant convex set – an inequality and applications . Proc. Amer. Math. Soc. 17 : 327 – 1333 .
- Mudholkar , G. S. ( 1969 ). A generalized monotone character of d.f.'s and moments of statistics from some well-known populations . Ann. Inst. Statist. Math. 21 : 277 – 285 .
- Mudholkar , G. S. , Natarajan , R. ( 2002 ). The inverse Gaussian models: analogues of symmetry, skewness and kurtosis . Ann. Instit. Statist. Math. 54 : 138 – 154 .
- Mudholkar , G. S. , Wang , H. ( 2007 ). IG-symmetry and R-symmetry: interrelations and applications to the inverse Gaussian theory J. Statist. Plann. Infer. 137 : 3655 – 3671 .
- Mudholkar , G. S. , Wang , H. , Natarajan , R. ( 2009 ). The G-IG analogies and robust tests for inverse Gaussian scale parameters . Proc. Int. Conf. Mathemat. Statist. Model. In press .
- Ostrowski , A. ( 1952 ). Sur quelques applications des fonctions convexes et concaves au sens de I. Schur . J. Mathmatiques Pures et Appliques 31 : 253 – 292 .
- Patil , S. A. , Kovner , J. L. ( 1979 ) On the power of an optimum test for the mean of the inverse Gaussian distribution . Technometrics 21 : 379 – 381 .
- Schrödinger , E. ( 1915 ). Zur theorie der fall-und steigversuche an teilchenn mit Brownsche bewegung . Physikalische Zeitschrift 16 : 289 – 295 .
- Seshadri , V. ( 1993 ). The Inverse Gaussian Distribution: A Case Study in Exponential Families . New York : Oxford University Press .
- Seshadri , V. ( 1999 ). The Inverse Gaussian Distribution: Statistical Theory and Applications . New York : Springer .
- Smoluchowski , M. V. ( 1915 ). Notiz über die Berechning der Brownschen Molkularbewegung bei des Ehrenhaft-millikanchen Versuchsanordnung . Physikalische Zeitschrift 16 : 318 – 321 .
- Tweedie , M. C. K. ( 1957a ). Some statistical properties of inverse Gaussian distributions I . Ann. Mathemat. Statist. 28 : 362 – 377 .
- Tweedie , M. C. K. ( 1957b ). Some statistical properties of inverse Gaussian distributions II . Ann. Mathemat. Statist. 28 : 696 – 705 .
- Woldie , M. , Folks , J. L. , Chandler , J. P. ( 2001 ). Power function for inverse Gaussian regression models . Commun. Statist. Theor. Meth. 30 : 787 – 797 .