normal_discrete (one dimensional)

subroutine normal_discrete(x, prob, mu, sigma)

Description:

This subroutine calculates the nodes and weights for an approximation of a one-dimensional normal distribution with mean and variance . We can use these nodes and weights, for example, to calculate moments as

It therefore uses the Gauss-Hermite quadrature method.

Output arguments:

• real*8 :: x(:)
  A one-dimensional array into which the subroutine stores the nodes for the Gauss-Hermite approximation.
• real*8 :: prob(:)
  A one-dimensional array into which the subroutine stores the weights or probabilities for the Gauss-Hermite approximation. Note that prob(:) needs to have exactly the same size as x(:).

Optional arguments:

• real*8 :: mu
  The mean of the normally distributed random variable. If not present, the mean is set to a value of 0.
• real*8 :: sigma
  The variance of the normally distributed random variable. If not present, the variance is set to a value of 1. This input value must be greater than or equal to zero, otherwise the subroutine throws an error message.

References

• Parts of this routine were copied and adapted from:
  • the Matlab codes provided in the CompEcon toolbox of Mario Miranda and Paul Fackler
• For further reading refer to:
  • Miranda, M. & Fackler, P. (2002). Applied Computational Economics and Finance. Cambridge: MIT Press.
  • Stoer, J. & Bulirsch, R. (2002). Introduction to Numerical Analysis. New York: Springer Text in Applied Mathematics.
  • Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. (1992). Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing, 2nd edition. Cambridge: Cambridge Univeristy Press.
• This routine is used in the following programs:
  • prog02_14.f90
  • prog10_04.f90
  • prog10_05.f90
  • prog10_06.f90