If you need an accessible version of this item please contact JSTOR User Support

Asymptotic Inversion of Incomplete Gamma Functions

N. M. Temme
Mathematics of Computation
Vol. 58, No. 198 (Apr., 1992), pp. 755-764
DOI: 10.2307/2153214
Stable URL: http://www.jstor.org/stable/2153214
Page Count: 10
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Asymptotic Inversion of Incomplete Gamma Functions
Preview not available

Abstract

The normalized incomplete gamma functions P(a, x) and Q(a, x) are inverted for large values of the parameter a. That is, x-solutions of the equations $P(a, x) = p, Q(a, x) = q, \quad p \in \lbrack 0, 1\rbrack, q = 1 - p,$ are considered, especially for large values of a. The approximations are obtained by using uniform asymptotic expansions of the incomplete gamma functions in which an error function is the dominant term. The inversion problem is started by inverting this error function term. Numerical results indicate that for obtaining an accuracy of four correct digits, the method can already be used for a = 2, although a is a large parameter. It is indicated that the method can be applied to other cumulative distribution functions.

Page Thumbnails

  • Thumbnail: Page 
755
    755
  • Thumbnail: Page 
756
    756
  • Thumbnail: Page 
757
    757
  • Thumbnail: Page 
758
    758
  • Thumbnail: Page 
759
    759
  • Thumbnail: Page 
760
    760
  • Thumbnail: Page 
761
    761
  • Thumbnail: Page 
762
    762
  • Thumbnail: Page 
763
    763
  • Thumbnail: Page 
764
    764