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Dokumentation

QF00_BETAI - Incomplete beta integral

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Task

The function module calculates the incomplete beta integral.

Example (Binomial distribution)

  DATA:
    N         TYPE I,
    K         TYPE I,
    P         TYPE F,
    PROB_BIN  TYPE F,
    V1        TYPE F,
    W1        TYPE F,

  V1 = K.
  W1 = N - K + 1.

  CALL FUNCTION 'QF00_BETAI'
    EXPORTING V      = V1
              W      = W1
              X      = P
    IMPORTING BETAI  = PROB_BIN.

Description

The incomplete beta integral is defined for v > 0 and w > 0 by the formula

BETAI(v,w,x) = INTEGRAL(0..x, t**(v-1) * (1-t)**(w-1) dt) / BETA(v.w)

This integral occurs in the calculation of t-distribution F-distribution, beta distribution and binomial distribution statistics.

Reference

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

Parameters

BETAI
ITERATIONEN
V
W
X

Exceptions

INVALID_X
NOT_POSITIVE

Function Group

QF00

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