Timeline for Why are the Lyapunov and Lindeberg Central Limit Theorem conditions often satisfied in the real world?
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| Oct 10, 2018 at 16:24 | comment | added | roobee | that was one of the questions i had found that wasn't very satisfying. the one upvote question wasn't very clear what it was saying. the 8 upvote question said that on average the lyapunov condition shows the moments of Y aren't too big which would have been useful if they explained how the lyapunov condition shows that. But they didn't. | |
| Oct 10, 2018 at 4:51 | comment | added | A Nejati | this answer explains it quite well. | |
| Oct 10, 2018 at 4:36 | comment | added | roobee | can you explain why if the variance of the sum doesn't diverge than lyapunov's condition is satisfied? | |
| Oct 6, 2018 at 23:09 | comment | added | A Nejati | What I wanted to get at with my answer though was that satisfying those conditions exactly isn't even critical - lots of systems that violate the conditions for the CLT in various ways still look close to normal, for the reasons I described. | |
| Oct 6, 2018 at 22:57 | comment | added | A Nejati | Lyapunov's condition shouldn't be unusual or surprising, it is merely to establish that the variance of the sum doesn't diverge. It is easy to see how in an approximate real-world scenario, with large but finite $N$, this condition would be satisfied. | |
| Oct 6, 2018 at 22:19 | comment | added | roobee | you say the CLT variant you linked shows that sums of mostly independent random variables with some uncertainty are also mostly normal. An explanation on why the mathematical conditions in the CLT variant you link approximately translate to -mostly independent random variables with some uncertainty - would also suffice if it would be clearer than an explanation of Lyapunov or Lindeberg conditions. | |
| Oct 6, 2018 at 21:45 | comment | added | roobee | "the CLT says that if you have a bunch of different independent random variables and you sum them, you get something that looks normal". That is actually one of the major points I was confused on. The closest variant of the CLT I could find that says something like that were the Lyapunov and Lindeberg variants. But they have complicated conditions that I am not sure why would often be satisfied in real-life. | |
| Oct 5, 2018 at 20:17 | history | answered | A Nejati | CC BY-SA 4.0 |