You can use any classification etc., database for your statistical distributional model, see e.g., the free publicly available databases : https://www.robots.ox.ac.uk/~vgg/data/ and CV-Data : https://www.visualdata.io/discovery

Did you check Kaggle, use the filters appropriately to find the right data set.

A Cauchy distribution is essentially distribution with all outliers. You might look at the references in the attached or in the work of Rand Wilcox at USC. Best, D. Booth

You also could try simulation, see the link: https://www.bing.com/search?q=design+of+simulation+experiments&cvid=85b40c0d7af24d608c24a2e27738646c&FORM=ANAB01&PC=U531

Best, D. Booth

I think you should test for Cauchy distribution of some stocks returns (SP500, DAX, CAC40, .....). This article could be helpful for you: https://reader.elsevier.com/reader/sd/pii/S1018364718313193?token=C1F9220C6ED243408D231CF71B9D66DEC00AB96AFE7647CBBC2CD0F2CC594C3B6930EB9FE648D86DADEBB6CBC7E2117F