Timeline for CLT for stationary sequences with infinite variance
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 18, 2009 at 9:54 | comment | added | Piotr Miłoś | I still not quite understand. The assumptions in the CLT are that that X_n are square integrable (loosely speaking) which more or less is eqivalent to the fact that their tails decays like o(t^{-2}). | |
| Nov 17, 2009 at 19:48 | comment | added | Jonathan Kariv | By nice properties I mean properties it would need to have to be considered an analog of the CLT | |
| Nov 17, 2009 at 18:21 | comment | added | Piotr Miłoś | I not quite understand. What do you mean by "nice properties"? Some properties of r.v. X_n? Or something else? In the first case I would like to assume about X_n as little as possible. Probably something about the tails decay. | |
| Nov 17, 2009 at 18:15 | comment | added | Michael Lugo | More generally, there are "stable distributions" (en.wikipedia.org/wiki/Stable_distribution) that have the property that a sum of n of them, scaled by n^(1/alpha), has the same distribution as the original. | |
| Nov 17, 2009 at 17:57 | history | answered | Jonathan Kariv | CC BY-SA 2.5 |