# Probability plot for Cauchy Distribution

• herjia

#### herjia

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?

-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?

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!