Cumulative Joint Bivariate Normal Probability Distribution with a given rho

[PaulN]

I want to calculate the cumulative bivariate normal distribution of two standard normal variables.  Is  there a SAS PROC or SAS FUNCTION that does this?  When rho=0, this is easy but rho =^ 0, it's more involved.  For example, suppose x1=-2.05 and x2=-1.64. -2.05 is associated 0.02 with and -1.64 is associated with 0.05.  When rho=0, you just multiply 0.02*0.05 to get 0.001 but when rho N=^ 0 it's a little messy.  Trying to avoid writing the code if SAS has a PROC of FUNCTION that does this for me.  No IML please.

[PaigeMiller]

No IML? Trying to avoid writing the code? There is the PROBBNRM function in SAS, but that's not a cumulative distribution. And from that point on, I think you either need to write your own code, or use IML.

Update: this answer is incorrect; see comment from @FreelanceReinh below

[FreelanceReinh]

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@PaigeMiller wrote:

There is the PROBBNRM function in SAS, but that's not a cumulative distribution.

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Hi @PaigeMiller, I think it is cumulative and hence ideal for PaulN's task.

(Thanks to Rick_SAS for mentioning the function recently enough so that I remembered it.)

[PaigeMiller]

@FreelanceReinh thanks for the correction!!!

[Ksharp]

Better calling @Rick_SAS 

[Rick_SAS · Accepted solution]

Yes, use the PROBBNRM function, which is in Base SAS. I describe the function and how to use it in the article "Visualize the bivariate normal cumulative distribution."

data CDF2D;
input rho x1 x2;
cdf = probbnrm(x1,x2,rho);
datalines;
0    -2.05 -1.64
0.5  -2.05 -1.64
-0.5 -2.05 -1.64
;

proc print data=CDF2D; run;

[PaulN]

Thank you for the help.  It's appreciated.