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Probability plot for Cauchy Distribution

  1. Mar 1, 2007 #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?
  2. jcsd
  3. Mar 3, 2007 #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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