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