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QF00_GAMMAI - Incomplete gamma integral

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Functionality

This function module is used to calculate an incomplete gamma integral.

Example (Poisson distribution)

Calculation of the distribution function of the Poisson distribution with parameter MU at position K.

  DATA:
    A1           TYPE F,
    K            TYPE I,
    MU           TYPE F,
    PROB_POISSON TYPE F,
    Q            TYPE F.

  A1 = K - 1.

  CALL FUNCTION 'QF00_GAMMAI'
    EXPORTING A      = A1
              X      = MU
    IMPORTING GAMMAI = Q.

  PROB_POISSON   =   1 - Q.

Notes

The incomplete gamma integral is defined by the following formula:

GAMMAI(a,x) = INTEGRAL(0..x, exp(-t) * t**(a-1) dt) / GAMMA(A)

where a > 0.

This integral is found in statistics when you calculate the Chi square distribution and Poisson distribution.

Further information

Literature

W.H.Press, B.P.Flannery, S.A.Teukolsky, W.T.Vetterling, Numerical Recipes in C, Cambridge University Press, Cambridge 1988

Parameters

A
GAMMAI
ITERATIONEN
X

Exceptions

INVALID_A

Function Group

QF00

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