Posted by mike osborn on October 10, 1997 at 14:22:09:

I'm loking for an efficient FORTRAN routine to

integrate the volume under a multi-dimensional

gaussian surface with arbitrary covariance

over definite (sometimes small) limits. I've

found the algorithm referenced below, but it does the

job from -infinity to a set of limits. For an n-D

calculation I think I have to do 2**n calls to this

routine to get the right answer (for example: to

integrate from X1 to X2 and Y1 to Y2, you have to call

DMV for X2,Y2 + X1,Y1 - X1Y2 - X2Y1).

Any suggestions?

reference:

C ALGORITHM 725, COLLECTED ALGORITHMS FROM ACM.

C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,

C VOL. 19, NO. 4, DECEMBER, 1993, P. 546.

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

C

C

C DMV CALCULATES THE MULTIVARIATE NORMAL INTEGRAL.

C

C THE INTEGRAL LOWER LIMITS ARE -INFINITY FOR ALL VARIABLES.

C THE UPPER LIMITS ARE GIVEN BY THE VECTOR H (INPUT).

C THE CORRELATION MATRIX IS R (INPUT).

- Re: integration of n-D gauss. dist for finite limits
**Michael Neale***15:36:03 11/06/97*(0)