General Saddlepoint Approximation for Testing Separate Location-Scale Families of Hypotheses

References

• Bain , L. J. , Engelhardt , M. ( 1980 ). Probability of correct selection of Weibull versus gamma based on likelihood ratio . Communications in Statistics – Theory and Methods 9 ( 4 ): 375 – 381 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O. E. , Cox , D. R. ( 1989 ). Asymptotic Techniques for Use in Statistics . London : Chapman and Hall .
   Google Scholar
• Barndorff-Nielsen , O. E. , Cox , D. R. ( 1994 ). Inference and Asymptotics . London : Chapman and Hall .
   Google Scholar
• Cox , D. R. ( 1961 ). Test of separate families of hypotheses . Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability 1 : 105 – 123 .
   Google Scholar
• Cox , D. R. ( 1962 ). Further results on tests of separate families of hypotheses . Journal of the Royal Statistical Society B 24 : 406 – 424 .
   Google Scholar
• Daniels , H. E. ( 1954 ). Saddlepoint approximations in statistics . Annals of Mathematical Statistics 25 : 631 – 650 .
   Google Scholar
• Ducharme , G. R. , Frichot , B. ( 2003 ). Quasi most powerful invariant goodness-of-fit tests . Scandinavian Journal of Statistics 30 : 399 – 414 .
   Web of Science ®Google Scholar
• Dumonceaux , R. , Antle , C. E. ( 1973 ). Discrimination between the log-normal and the Weibull distributions . Technometrics 15 : 923 – 926 .
   Web of Science ®Google Scholar
• Dumonceaux , R. , Antle , C. E. , Haas , G. ( 1973 ). Likelihood ratio test for discrimination between two models with unknown location and scale parameters . Technometrics. 15 : 19 – 31 .
   Web of Science ®Google Scholar
• Easton , G. S. , Ronchetti , E. ( 1986 ). General saddlepoint approximations with application to L statistics . Journal of the American Statistical Association 81 : 420 – 430 .
   Web of Science ®Google Scholar
• Fearn , D. H. , Nebenzahl , E. ( 1990 ). On the maximum likelihood ratio method of deciding between the Weibull and gamma distributions . Communications in Statistics – Theory and Methods 20 ( 2 ): 579 – 593 .
   Web of Science ®Google Scholar
• Franck , W. E. (1981). The most powerful invariant test of normal versus Cauchy with applications to stable alternatives. Communications in Statistics — Theory and Methods 76:1002–1005.
   Google Scholar
• Gatto , R. , Ronchetti , E. ( 1996 ). General saddlepoint approximations of marginal densities and tail probabilities . Journal of the American Statistical Association 91 : 666 – 673 .
   Web of Science ®Google Scholar
• Gradshteyn , I. S. , Ryzhik , I. M. ( 2000 ). Table of Integrals, Series, and Products. , 6th ed. San Diego: Academic Press .
   Google Scholar
• Gupta , R. D. , Kundu , D. ( 2003 ). Discriminating between Weibull and generalized exponential distributions . Computational Statistics & Data Analysis 43 : 179 – 196 .
   Web of Science ®Google Scholar
• Gupta , R. D. , Kundu , D. ( 2004 ). Discriminating between gamma and generalized exponential distributions . Journal of Statistical Computation & Simulation 74 : 107 – 121 .
   Web of Science ®Google Scholar
• Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1994 ). Continuous Univariate Distributions . Vol. 1 . New York : Wiley .
   Google Scholar
• Johnson , N. L. , Kotz , S. , Balakrishnan , N. ( 1995 ). Continuous Univariate Distributions . Vol. 2 . New York : Wiley .
   Google Scholar
• Lehmann , E. L. ( 1986 ). Testing Statistical Hypotheses . New York : Wiley .
   Google Scholar
• McCullagh , P. ( 1987 ). Tensor Methods in Statistics . London : Chapman and Hall .
   Google Scholar
• Otsu , T. ( 2005 ). Testing normality against the Laplace distribution . Journal of Modern Applied Statistical Methods 4 : 402 – 407 .
   Google Scholar
• Reid , N. ( 1988 ). Saddlepoint methods in statistical inference (with discussion) . Statistical Science 3 : 213 – 238 .
   Google Scholar
• Reid , N. ( 1991 ). Approximations and asymptotics . In: Hinkley , D. V. , Reid , N. , Snell , E. J. , eds. Statistical Theory and Modeling, In Honor of Sir David Cox, FRS. . London : Chapman and Hall .
   Google Scholar
• Wang , S. ( 1992 ). General saddlepoint approximations in the bootstrap . Statistics & Probability Letters 13 : 61 – 66 .
   Web of Science ®Google Scholar
• White , H. ( 1982 ). Regularity conditions for Cox's test of non-nested hypotheses . Journal of Econometrics 19 : 301 – 318 .
   Web of Science ®Google Scholar