Hi lately I was focused on theoretical modeling of heavy-tailed data. However, I find it hard to collect some classic heavy-tailed data for experiments. I wonder if there is any public and well-known (better if any) dataset confirmed to be heavy-tailed from Kaggle or some labs ?
I'd start with Log-normal, and then going to this page, you see sources for this distribution:
Let's pick one of the easier ones to find: Length of Spoken Words. (Note that written words is not lognormal - source.)
And to keep it relevant, there is good structured data for US Presidential (Campaign) speeches. You mentioned Kaggle, so here is one example:
Collection of data from the 2016 U.S. Presidential Election Campaign containing:
1 Transcripts of the three presidential debates, divided into separate Trump and Clinton text files
2 Transcripts of Trump's 64 speeches delivered after the RNC and Clinton's 35 speeches delivered after the DNC
3 Transcripts of select speeches delivered by candidates during the primary campaigns
4 USC Dornsife/LA Times Presidential Election Poll, with daily breakdown by voter groups
5 Five Thirty Eight Election Poll, containing daily data from numerous pollsters
1, 2 or 3 would work.
For the record, there are MANY ways of collecting heavy-tailed data, and this is just an example of one way to get started...
for fun, quick analysis from 2016 election: