topic Re: Random Number Generating in SAS/IML Software and Matrix Computations

Random Number Generating

trash — Sat, 11 Nov 2017 23:06:15 GMT

I'm given these two equations:

PDF: f(x) =1/(π(1+x^2)) -∞ ≤ x ≤ ∞ CDF: F(x) =(1/2) + arctan(x)/π -∞ ≤ x ≤ ∞

and I am asked to generate 10,000 random numbers using the Inversion Method for Cauchy Distribution.

Here is the code I have started:

PROC IML;
n=10000;
myran = j(n,1, 0);
uniform = uniform(myran);
exponential = (tan(uniform*pi-(pi/2)));

CREATE uniform2 FROM uniform[colname={'x'}];
APPEND FROM uniform;
CREATE exp2 FROM exponential[colname={'y'}];
APPEND FROM exponential;
QUIT;

but my log says: "ERROR: (execution) Matrix has not been set to a value." after the exponential statement.

how do I correct for this? I'm not sure how to account for the -∞ ≤ x ≤ ∞ part.

subsequently, I am asked to create a subset of the 10000 Cauchy Dist. of random numbers where -10<x<10

WarrenKuhfeld — Sun, 12 Nov 2017 01:14:49 GMT

Set the scalar pi to a value after you invoke IML.

pi = constant('pi');

Ksharp — Sun, 12 Nov 2017 11:26:38 GMT

IML has build-in function, you can use it .

proc iml;
x=j(10000,1,.);
call randseed(12345678);
call randgen(x, 'CAUCHY'); 

create want var{x};
append;
close;
quit;

Rick_SAS — Sun, 12 Nov 2017 12:02:44 GMT

You asked, "how do I account for the [-infinity, infinity] part?" Here is a hint: What is the range of the expression

uniform*pi - pi/2 ?

Ask yourself how the TAN function behaves on this interval.

For more about the inverse CDF method of simulating data, see "The inverse CDF method for simulating from a distribution."