You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Asymptotic Inversion of Incomplete Gamma Functions
N. M. Temme
Mathematics of Computation
Vol. 58, No. 198 (Apr., 1992), pp. 755-764
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2153214
Page Count: 10
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
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.
Mathematics of Computation © 1992 American Mathematical Society