32
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

A new simple straightforward and practical asymptotic expansion for the incomplete beta function

Pages 227-243 | Received 12 Aug 1986, Published online: 20 Mar 2007

References

  • Hill , G. W. 1969 . Progress results on asymptotic approximations for Student's t and chi-squared Unpublished manuscript ∗His results however were quoted by E. A. Cornish at the Fisher Memorial Lecture 1969, 37th Session, I.S.I., London.
  • Molinaar , W. 1970 . “ Mathematical centre tracts no. 31, mathematisch centrum ” . In Approximations to the poisson, binomial and hypergeometric distribution functions , Amsterdam† . See p. 102, Eq. 5.12, choosing ∊1 = 1/45≈0.022 and ∊2 =2/150≈0.133.
  • Peizer , D. B. and Pratt , J. W. 1968 . A normal approximation for binomial, f, beta and other common related tail probabilities, part I . J.Amer.Statist.Assoc , 63 : 1416 – 1456 .
  • Pratt , J. W. 1968 . A normal approximation for binomial, F, beta and other common related tail probabilities, part II . J.Amer.Statist.Assoc , 63 : 1457 – 1483 .
  • Schell , H. J. 1980a . Asymptotische entwicklunger für die unvollständige gammafunktion . Wiss.Zeits.Tech.Hoch , 22 : 477 – 485 .
  • Schell H. J. Gleichmässige asymptotischedurstellungen und entwicklungen von parameterintegralen mit zwei reellen parametern 1980b Dissertation, B. Karl Marx Stadt
  • Schell , H. J. 1983a . Gleichmässige asymptotische entwicklungen fur parameter-integrale mit zwei reellen parametern . Zeit.Anal.Anwend , 2 ( 1 ) : 159 – 173 .
  • Schell , H. J. 1983b . Gleichmässige asymptotische entwick lungen für Unvollständige integrale . Zeit.Anal.Anwend , 2 ( 5 ) : 427 – 442 .
  • Temme , N. M. 1982 . The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions . SIAM J.Math.Anal , 13 ( 5 ) : 239 – 252 .
  • Temme , N. M. 1985 . “ Centrum voor wiskunde en information ” . In Incomplete laplace integrals: uniform asymptotic expansions with application to the incomplete beta function , Amsterdam .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.