Expressions for the normal distribution and repeated normal integrals

Statistics and Probability Letters

Volumn 76, Issue 5, 2006, Pages 479-487

  Withers, C S ^a   McGavin, P N ^a  

^a CALLAGHAN INNOVATION   (New Zealand)

Author keywords

Airey functions; Hermite functions; Laplace's expansion; Mills' ratio; Normal distribution; Repeated integrals; Univariate

Indexed keywords

EID: 32544437539     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2005.08.015     Document Type: Article

References (13)

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2. Airey, J.R., 1931. Table of Hh functions, Table XV, Mathematical Tables 1. second ed. 1946, third ed. 1951. British Association for the Advancement of Science, London, pp. 60-72.
3. Y. Chou D.B. Owen An approximation to percentiles of a variable of the bivariate normal distribution when the other variable is truncated with applications Comm. Statist. Theory Methods 13 20 1984
4. L. Comtet Advanced Combinatorics 1974 Reidel Dordrecht
5. Fisher, R.A., 1931. Introduction of Table of Hh functions, of Airey (1931), Mathematical Tables, vol. 1, second ed. 1946, third ed. 1951. British Association for the Advancement of Science, London, pp. xxvi-xxxvii
6. I.S. Gradshteyn I.M. Ryzhik Tables of Integrals Series and Products fourth ed. 1965 Academic Press New York
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9. Kotz, S., Balakrishnan, N., Johnson, N.L., 2000. Continuous Multivariate Distributions, vol. 1, second ed. Wiley, New York.
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11. J.F. Mills Table of the ratio: Area to bounding ordinate for any portion of normal curve Biometrika 18 1926 395-400
12. D.B. Owen Handbook of Statistical Tables 1962 Addison-Wesley Reading, MA
13. C.S. Withers A simple expression for the multivariate Hermite polynomials Statist. Probab. Lett. 47 2000 165-169