GammaCDF

function GammaCDF(x, alpha, beta)

Description:

Calculates the cumulative distribution function

of the Gamma distribution with shape and rate . denotes the lower incomplete gamma function.

Input arguments:

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

Optional arguments:

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

Return Value:

• real*8 :: GammaCDF
  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 ASA239.
• For further reading refer to:
  • Toral, R. & Colet, P. (2014). Stochastic Numerical Methods: An Introduction for Students and Scientists. Weinheim: Wiley.
  • Shea, B. (1988). Algorithm AS 239: Chi-squared and Incomplete Gamma Integral, Applied Statistics, 37(3), 466-473.
• This routine is used in the following programs:
  • prog02_15.f90