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A FORTRAN routine for the computation of gamma percentiles. (English) Zbl 0649.65017

The topic is the inverse problem for gamma distribution, i.e., for given $a\left(>0\right)$ and $p\left(0, to find x such that

$p=P\left(a,x\right)=1/{\Gamma }\left(a\right){\int }_{0}^{x}{e}^{-t}{t}^{a-1}dt·$

The author gives an algorithm and its FORTRAN program. The method is to solve the equation $P\left(a,x\right)-p=0$ 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 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.

Reviewer: S.Hitotumatu
##### MSC:
 65D20 Computation of special functions, construction of tables 65C99 Probabilistic methods, simulation and stochastic differential equations (numerical analysis) 33B15 Gamma, beta and polygamma functions 62G99 Nonparametric inference