Probability plot for Cauchy Distribution

  • #1
I have generated 2 columns of normal random variables, Z1 and Z2. Theorectically, Z1/Z2 will follow a Cauchy distribution. The question is, how do I construct a probability plot to show that indeed it is a Cauchy distribution?

I tried the follow procedure:
-Sort the Z1/Z2
-Rank them and store the rank on a new column, i
-perform median rank (herd-Johnson) i/n+1 where n is the sample size
-perform inverse cumulative probability on the median rank column
-plot the z1/z2 vs inverse cumulative probability

What i get is near the location, the data are linear while the deviation is serious at either extreme ends. any suggestion? or references?
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  • #2
It's very very very important that the two standard normal variables you generated are independent. I don't know how you generated them so I don't know if they are.

It also goes without saying that you're going to need a sizeable amount of data to get anything meaningful.

Personally, I'd just prove that Z1/Z2 is a Cauchy distribution. It's fun!

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