References
- Abramowitz , M. and Stegun , I. 1972 . Handbook of Mathematical Functions New York, NY : Dover, Publications .
- DeLong , D. M. and Guirguis , G. H. 1994 . Gauss-Laguerre dynamics: An efficient method of computing integrals in multiple comparisons . Commun. Statist., Part B – Simul. Comput. , 23 : 1047 – 1059 .
- Fritsch , K. S. and Hsu , J. C. 1997 . “ Multiple comparisons with the mean (STMA V39 4596) ” . In Advances in Statistical Decision Theory and Applications (Statistics for Industry and Technology) Edited by: Panchapakesan , S. and Balakrishnan , N. 189 – 204 . Boston : Birkhauser .
- Gautschi , W. 1969 . ACM algorithm 363: Complex error function . Commun. ACM , 12 : 635
- Guirguis , G. and Tobias , R. D. 1990 . Generalization and efficient computation of the Box-Meyer analysis for orthogonal designs . Commun. Statist., Part B – Simul. Comput. , 19 : 721 – 732 .
- Nelson , P. R. 1981 . Numerical evaluation of an equicorrelated multivariate non-central t distribution . Commun. Statist., Part B — Simul. Comput. , 10 : 41 – 50 .
- Nelson , P. R. 1982a . An approximation for the complex normal probability integral . BIT , 22 ( 1 ) : 94 – 100 .
- Nelson , P. R. 1982b . Exact critical points for the analysis of means . Commun. Statist., Part A – Theory Methods , 11 : 699 – 709 .
- Nelson , P. R. 1988 . Application of the analysis of means . Proc. SAS Users Group Int. Conf. , 13 ( 13 ) : 225 – 230 .
- Nelson , P. R. 1991 . “ Numerical evaluation of multivariate normal integrals with correlations ρ lj = − α l α j ” . In The Frontiers of Statistical Scientific Theory and Industrial Applications. Vol. II , Proceedings of the ICOSCO-I Conference 97 – 114 . Columbus : American Sciences Press, Inc. .
- Nelson , P. R. 1993 . Additional uses for the analysis of means and extended tables of critical values . Technometrics , 35 : 61 – 71 .
- Poppe , G. P. M. and Wijers , C. M. J. 1990 . Algorithm 680: Evaluation of the complex error function . ACM Trans. Math. Software , 16 : 147
- Rice , S. O. 1973 . Efficient evaluation of integrals of analytic functions by the trapezoidal rule . Bell Sys. Tech. J. , 52 ( 5 ) : 707 – 722 .
- SAS Institute Inc. (2003). SAS/QC User's Guide
- Sikorsky , K. 1982 . Optimal quadrature algorithms in H p spaces . Num. Mat. , 39 : 405 – 410 .
- Sikorsky , K. and Stenger , F. 1984 . Optimal quadratures in H p spaces . ACM, Toms , 10 : 140 – 151 . June
- Soong , W. C. and Hsu , J. C. 1997 . Using complex integration to compute multivariate normal probabilities . J. Comput. Graphical Statist. , 6 : 397 – 415 .
- Squire , W. 1987 . “ Comparison of Gauss-Hermite and midpoint quadrature with the application of the Voigt function ” . In Numerical Integration: Recent Developments , (NATO ASI Series, Ser. C: Vol. 204) Edited by: Keast , P. and Fairweather , G. 111 – 112 . Boston : Reidel .
- Stenger , F. 1973 . Integration formulas based on the trapezoidal formula . J. Inst. Math. Appl. , 12 : 103 – 114 .
- Stenger , F. 1977 . Remarks on integration formulas based on the trapezoidal formula . J. Inst. Math. Appl. , 19 : 145 – 147 .
- Stenger , F. 1978 . Optimal convergence of minimum norm approximations in H p . Num. Mat. , 29 : 345 – 362 .
- ‡To the memory of Professor Peter Nelson.