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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(>0) and p(0<p<1), to find x such that

p=P(a,x)=1/Γ(a) 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(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 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:
65D20Computation of special functions, construction of tables
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
33B15Gamma, beta and polygamma functions
62G99Nonparametric inference