Erol asked . 2022-06-09

How to generate samples from a cauchy distribution

For an assignment I have to draw samples of different sizes from a Cauchy distribution in order to show that as the sample size increases, the mean does not tend to any number (therefore the mean does not exist). However, I have been having trouble trying to figure out how to properly create my Cauchy distribution.

Knowing that a cauchy distribution is simply a variable computed using the ratio of two independent standard normal variables, I created two standard normal variables and then divided them to create this new Cauchy variable. I then found the sample mean, and repeated the process for sample sizes of 10, 100, 500, 1000, 5000, and 10,000.

The following code is the same process that I used for each sample size:

a_c1= randn(10,1)
a_c2= randn(10,1)
a_c1ovrc2=a_c1/a_c2
a_c1ovrc2( :, ~any(a_c1ovrc2,1) )= [] %in order to delete all the unnecessary zero columns(I don't understand why they were created in the first place)
a_c1ovrc2_m = mean(a_c1ovrc2)

cauchy-distribution

The above table are the values i obtained after completing each operation separately. I don't feel like this accurately shows that the Cauchy distribution has no mean. Any advice as to what I might be doing wrong would be sincerely appreciated!

cauchy distribution , standard normal , AI, Data Science, and Statistics , Statistics and Machine L

Expert Answer

Kshitij Singh answered . 2024-12-21 01:15:27

a_c1ovrc2( :, ~any(a_c1ovrc2,1) )= []

"in order to delete all the unnecessary zero columns(I don't understand why they were created in the first place)"

They came from the preceding line

a_c1ovrc2=a_c1/a_c2;

HINT: See

doc ./  % follow links to "Arithmetic Operators" at bottom

After perusing these, all should become clear...

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