Program for bivariate distribution for f(x, y) = 1/pi where x^2 + y^2 = 1

[joesocci]

(a) [10] Write a program to draw 100,000 observations from the following bivariate distribution which is uniform over a unit circle. f(x, y) = 1/ℼ where x2 + y2 < 1

(b) [10] Draw the bivariate histogram for x and y. (c) [10] Draw the (marginal) histogram for x .

I've tried transforming x and y so that they vary between (-1,1) and then using the Do while loop so that x2 + y2< 1. Still new to SAS so any would be great.

This is my code so far:

data test;
    Do i=1 to 10000;
        Do While x^2 + b^2 <1;
            x=2*ranuni(111)-1;
            y=2*ranuni(111)-1;
            z= x^2 + b^2 <1;
        end;
        output;
    end;
run;
ods graphics on;
proc bivariatete data=test;
      var x;
      var y;
      var z;
      histogram z;
  run;
ods graphics off;

[Reeza]

This is invalid:

x^2

In SAS, the correct operator is **

x**2

http://support.sas.com/documentation/cdl/en/lrcon/69852/HTML/default/viewer.htm#p00iah2thp63bmn1lt20...

For the histogram, use PROC UNIVARIATE or PROC SGPLOT.

PS. You have a lot of other errors in your code. I would suggest doing one step at a time, getting that working and then moving forward. Look at Rick Wicklin blog or book for informaiton on how to simulate data in SAS. If you're a student, since this is clearly homework, your university library may have a digital version available for you to peruse.

[joesocci]

Thank you, I've gotten both x and y to vary between (-1,1), I'm still struggling to restrict it so that x^2 + y^2 <1 and output that data. Any suggestions or help would be appreciated!

[Ksharp]

It is about data simulation, better post it at IML forum.

what doest f(x,y) looks like,what is its form ?

[Ksharp]

You mean this ?

http://blogs.sas.com/content/iml/2016/03/30/generate-uniform-2d-ball.html

[Rick_SAS]

In addition to the excellent responses from @Reeza and @Ksharp, use PROC KDE to draw the bivariate histogram. The BIVAR statement and PLOTS=HISTOGRAM are what you want to use.