ON THE NULL DISTRIBUTIONS OF THE ENTROPY TESTS FOR THE GAUSSIAN AND INVERSE GAUSSIAN MODELS

REFERENCES

• Vasicek , O. 1976 . A test for normality based on sample entropy . J. R. Statist. Soc. B , 38 : 54 – 59 .
   Google Scholar
• Mudholkar , G. S. and Tian , L. 1999 . “ An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit test ” . In Tech. Rep., University of Rochester Rochester, NY Submitted for publication
   Google Scholar
• Mudholkar , G. S. and Kollia , G. D. 1991 . A graphical procedure for comparing goodness-of-fit tests . J. R. Statist. Soc. B , : 221 – 232 .
   Google Scholar
• Schrödinger , E. 1915 . Zür Theorie der Fall-und Steigversuche an Teilchenn mit Brownche Bewegung . Physikalische Zeitschrift , 16 : 377 – 382 .
   Google Scholar
• Smoluchowski , M. V. 1915 . Notizüber die Berechning der Brownshen Molkular-bewegung bie des Ehrenhaft-Milikanchen Versuchsanordnung . Physikalische Zeitschrift , 16 : 318 – 321 .
   Google Scholar
• Tweedie , M. C.K. 1945 . Inverse statistical variates . Nature , 155 : 453
   Web of Science ®Google Scholar
• Wald , A. 1947 . Sequential Analysis New York : Wiley .
   Google Scholar
• Chhikara , R. S. and Folks , J. L. 1989 . The Inverse Gaussian Distribution New York : Marcel Dekker .
   Google Scholar
• Seshadri , V. 1993 . The Inverse Gaussian Distribution: A Case Study in Exponential Families Oxford : Clarendon Press .
   Google Scholar
• Seshadri , V. 1999 . The Inverse Gaussian Distribution: Statistical Theory and Applications New York : Springer-Verlag .
   Google Scholar
• Folks , J. L. and Chhikara , R. S. 1978 . The inverse Gaussian distribution and its statistical application – a review . Journal of the Royal Statistical Society Series B , 40 : 263 – 289 .
   Google Scholar
• Iyengar , S. and Patwardhan , G. 1988 . “ Recent developments in inverse Gaussian distribution ” . In Handbook of Statistics Edited by: Krishnaiah , P. R. and Rao , C. R. Vol. 7 , 479 – 480 .
   Google Scholar
• Mudholkar , G. S. and Natarajan , R. 1998 . “ The inverse Gaussian analogs of symmetry, skewness and kurtosis ” . In Tech. Rep., University of Rochester Rochester, NY Accepted by Annals of the Institute of Statistical Mathematics
   Google Scholar
• Dudewicz , E. J. and van der Meulen , E. C. 1981 . Entropy-based test for uniformity . J. Amer. Statist. Assoc. , 76 : 967 – 974 .
   Web of Science ®Google Scholar
• Mudholkar , G. S. and Lin , C. C. 1984 . “ On two applications of characterization theorems ” . In colloquia mathematica societatis János Bolyai, vol 45. Goodness-of-fit, Debrecen (Hungary) 395 – 414 .
   Google Scholar
• Gokhale , D. V. 1983 . On entropy-based goodness-of-fit tests . Compu. Statist. & Data Analy. , 96 : 157 – 165 .
   Google Scholar
• Cressie , N. 1976 . On the logarithms of high-order spacings . Biometrika , 63 : 343 – 355 .
   Web of Science ®Google Scholar
• Dudewicz , E. J. and van der Meulen , E. C. 1987 . “ The empirical entropy, a new approach to nonparametric entropy estimation ” . In New Perspectives in Theoretical and Applied Statistics 207 – 227 . New York : Wiley .
   Google Scholar
• Hall , P. 1984 . Limit theorems for sums of general functions of m-spacings . Math. Statist. & Data Analy. , 1 : 517 – 532 .
   Google Scholar
• Hall , P. 1986 . On powerful distributional tests on sample spacings . J. Multivariate. Anal. , 19 : 201 – 255 .
   Web of Science ®Google Scholar
• Khashimov , S. A. 1989 . Asymptotic properties of functions of spacings . Theory Prob. Appl. , 34 : 298 – 307 .
   Google Scholar
• van Es , B. 1992 . Estimating fuctionals related to a density by a class of statistics based on spacings . Scand. J. of Statist. , 19 : 61 – 72 .
   Web of Science ®Google Scholar
• Michael , J. R. , Schucany , W. R. and Hass , R. W. 1976 . Generating random variables using transformation with multiple roots . American Statistician , 30 : 88 – 90 .
   Web of Science ®Google Scholar
• Lin , C. C. and Mudholkar , G. S. 1980 . A simple test for normality against asymmetric alternatives . Biometrika , 67 : 455 – 461 .
   Web of Science ®Google Scholar
• Mudholkar , G. S. , Natarajan , R. and Chaubey , Y. P. 1998b . “ Independence characterization and inverse Gaussian goodness-of-fit composite hypothesis ” . In Technical Report, University of Rochester Rochester, NY Submitted for publication
   Google Scholar
• Mudholkar , G. S. and Natarajan , R. 1999 . “ Moments-based goodness-of-fit tests for the inverse Gaussian models ” . In Tech. Rep., University of Rochester Rochester, NY Submitted for publication
   Google Scholar