A Likelihood-Based Approximation to the Cumulative Distribution Function of the Noncentral t Distribution

References

• Barndorff-Nielsen , O. E. ( 1986 ). Inference on full and partial parameters based on the standardized signed log-likelihood ratio . Biometrika 73 : 307 – 322 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O. E. ( 1991 ). Modified signed log-likelihood ratio statistic . Biometrika 78 : 557 – 563 .
   Web of Science ®Google Scholar
• Barndorff-Nielsen , O. E. , Cox , D. R. ( 1994 ). Inference and Asymptotics . London : Chapman and Hall .
   Google Scholar
• Broda , S. , Paolella , M. ( 2007 ). Saddlepoint approximations for the doubly noncentral t distribution . Computational Statistics and Data Analysis 51 : 2907 – 2918 .
   Web of Science ®Google Scholar
• DiCiccio , T. J. , Martin , M. A. ( 1991 ). Approximations of marginal tail probabilities for a class of smooth functions with applications to Bayesian and conditional inference . Biometrika 78 : 891 – 902 .
   Web of Science ®Google Scholar
• DiCiccio , T. J. , Field , C. A. , Fraser , D. A. S. ( 1990 ). Approximations of marginal tail probabilities and inference for scalar parameters . Biometrika 77 : 77 – 95 .
   Web of Science ®Google Scholar
• Fraser , D. A. S. ( 1990 ). Tail probabilities from observed likelihoods . Biometrika 77 : 65 – 76 .
   Web of Science ®Google Scholar
• Fraser , D. A. S. , Reid , N. , Wong , A. ( 1991 ). Exponential linear model: a two-pass procedure for saddlepoint approximation . Journal of the Royal Statistical Society B 53 : 483 – 492 .
   Google Scholar
• Lugannani , R. , Rice , S. ( 1980 ). Saddlepoint approximation for the distribution of the sum of independent random variables . Advanced Applied Probability 12 : 475 – 490 .
   Web of Science ®Google Scholar
• Rekkas , M. , She , Y. , Sun , Y. , Wong , A. ( 2008 ). An interesting application of a likelihood-based asymptotic . Journal of Applied Probability and Statistics 3 : 275 – 285 .
   Google Scholar
• Tierney , L. , Kass , R. E. , Kadane , J. B. ( 1989 ). Approximate marginal densities of nonlinear functions . Biometrika 76 : 425–433. Amendment (1991), 78 : 233 – 234 .
   Web of Science ®Google Scholar
• Wong , A. ( 2008 ). Approximating the F distribution via a general version of the modified signed log-likelihood ratio statistic . Computational Statistics & Data Analysis 53 : 3902 – 3912 .
   Web of Science ®Google Scholar