Timeline for Convergence of moments implies convergence to normal distribution
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 27, 2012 at 7:00 | vote | accept | Greg Martin | ||
| Jul 26, 2012 at 15:04 | comment | added | Ian Morris | Oops, I was looking at the wrong book by Billingsley! The result required to show that the normal distribution is characterised by its moments is also in the book Mateusz suggests, as Theorem 30.1. | |
| Jul 26, 2012 at 14:57 | comment | added | Mateusz Wasilewski | @Ian: it is an assumption of this theorem that distribution of limit is characterized by its moments. Without this, it is clearly false, because we can take two random variables $X$ and $Y$ which have different distributions and equal moments, and then just take $X_{n} \equiv Y$. | |
| Jul 26, 2012 at 13:37 | comment | added | Mark Meckes | @Ian: The English edition I own (third edition, 1995) has 38 sections grouped into 7 chapters. The theorem Mateusz refers to is also Theorem 30.2 on p. 390 of my copy. | |
| Jul 26, 2012 at 10:53 | comment | added | Ian Morris | The English editions only have 24 chapters, so I'm not sure what result this is. It seems to me that the difficult part is showing that the limit is characterised by its moments (which is false for certain distributions). | |
| Jul 26, 2012 at 8:41 | history | answered | Mateusz Wasilewski | CC BY-SA 3.0 |