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Zbl 0649.65017
Phien, Huynh Ngoc
A FORTRAN routine for the computation of gamma percentiles. (English)
[J] Adv. Eng. Softw. 10, No.3, 159-164 (1988). ISSN 0141-1195

The topic is the inverse problem for gamma distribution, i.e., for given $a(>0)$ and $p(0<p<1)$, to find x such that $$ p=P(a,x)=1/\Gamma (a)\int\sp{x}\sb{0}e\sp{-t}t\sp{a-1}dt. $$ The author gives an algorithm and its FORTRAN program. The method is to solve the equation $P(a,x)-p=0$ with a combination of the third-order Schröder iteration and the Newton-Raphson method. The initial value is given by the Wilson-Hilferty transformation (subroutine WILSON), and the incomplete gamma function (subroutine GAMAIN) is computed by using the algorithm of {\it Moore} [Algorithm AS187; Applied statistics 31(3), 330 (1982)]. The author shows an application example on the annual peak discharges of a water-fall, which gives a nice numerical result in few iterations.
[S.Hitotumatu]

MSC 2000:: *65D20 Computation of special functions
65C99 Numerical simulation
33B15 Gamma-functions, etc.
62G99 Nonparametric inference

Keywords: gamma percentiles; frequency analysis; gamma distribution; algorithm; FORTRAN program; third-order Schröder iteration; Newton-Raphson method; Wilson-Hilferty transformation; incomplete gamma function

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