betaCDF

function betaCDF(x, p, q)

Description:

Calculates the cumulative distribution function

of the beta distribution with shape parameters and . denotes the beta function

Input arguments:

• real*8 :: x
  The point where to evaluate the cumulative distribution function of the beta distribution.

Optional arguments:

• real*8 :: p
  Shape parameter. If not present, the function uses p = 1. Note that this input variable needs to be strictly greater than zero.
• real*8 :: q
  Shape parameter. If not present, the function uses q = 1. Note that this input variable needs to be strictly greater than zero.

Return Value:

• real*8 :: betaCDF
  The value of the cumulative distribution function at x.

References

• Parts of this routine were copied and adapted from:
  • Fortran Code by John Burkardt available as Algorithm ASA245.
  • Fortran Code by John Burkardt available as Algorithm ASA063.
• For further reading refer to:
  • Toral, R. & Colet, P. (2014). Stochastic Numerical Methods: An Introduction for Students and Scientists. Weinheim: Wiley.
  • Majumder, K.L. & Bhattacharjee, G.P. (1973). Algorithm AS 63: The incomplete Beta Integral, Applied Statistics, 22(3), 409-411.
  • Macleod, A.J. (1989). Algorithm AS 245: A Robust and Reliable Algorithm for the Logarithm of the Gamma Function. Applied Statistics, 38(2), 397-402.
• This routine is used in the following programs:
  • prog02_15.f90