options crt ;
name bivar 'Example of Approximating a Bivariate Normal Distribution' ;
?
?   TSP 4.2A (Sept 1992)
?   Author: Clint Cummins
?
SMPL 1,100;
?
?     This equation approximates a standard bivariate normal 
?  distribution with zero means and correlation coefficient rho.  
?  It's from Abramovitz and Stegun, Handbook of Mathematical Functions,
?  formula 26.3.29.
?
frml biv pr = cnorm(XB1)*cnorm(XB2) + norm(XB1)*norm(XB2)*(
           rho + rho**2*XB1*XB2/2 + rho**3*(XB1**2 - 1)*(XB2**2 - 1)/6 );
READ(NROW=2,TYPE=SYM) COV;
 1
.1 1 ;
DO RHO = .1 TO .91 BY .1;
  SET COV(2,1) = RHO;
  RANDOM(VCOV=COV) XB1 XB2;
  GENR BIV;
  PRINT RHO;
?
?     CDF computes the "true" bivariate normal distribution.
?
  CDF(BIVNORM,RHO=RHO) XB1 XB2 TRUE;
?  
?     Compute the approximation error and print statistics on it.
?
  APPERR = TRUE - PR;
  MSD APPERR;
ENDDO;
stop ; end ;