Timeline for Intuitive reason why jointly normal and uncorrelated imply independence
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 23, 2018 at 5:16 | history | edited | kjetil b halvorsen♦ |
edited tags
|
|
| Sep 27, 2017 at 14:02 | history | tweeted | twitter.com/StackStats/status/913041132162093057 | ||
| Sep 25, 2017 at 13:33 | comment | added | whuber♦ | Any deep reason is unlikely to be forthcoming, simply because there exist a large number of other examples of this phenomenon. Simply take any family $\{F_\theta\mid\theta\in\Theta\}$ of univariate distributions and embed that in a larger family of bivariate distributions $\{G_{\theta_1,\theta_2,\omega}\mid\theta_i\in\Theta,\omega\in\mathbb{R}\}$ for which $G_{\theta_1,\theta_2,0}(x,y)=F_{\theta_1}(x)F_{\theta_2}(y)$ and where $G_{\theta_1,\theta_2,\omega}$ for $\omega\ne 0$ has nonzero correlation coefficient. By construction, uncorrelated implies independent in such a family. | |
| Sep 25, 2017 at 12:07 | comment | added | Ashok | @DJohnson: I mean Pearson correlation. Please also see the edits. Thanks. | |
| Sep 25, 2017 at 12:05 | history | edited | Ashok | CC BY-SA 3.0 |
added 840 characters in body
|
| Sep 25, 2017 at 11:58 | comment | added | user78229 | I think you need to define your assumption wrt uncorrelated. The commonsense use of the word refers to Pearson correlation, a metric of strictly linear relationship. Many other measures of dependence are out there. So, two random variables may be uncorrelated wrt Pearson and still be highly dependent wrt other measures of association and dependence. | |
| Sep 25, 2017 at 11:47 | answer | added | kjetil b halvorsen♦ | timeline score: 10 | |
| Sep 25, 2017 at 11:16 | history | edited | kjetil b halvorsen♦ |
edited tags
|
|
| Sep 25, 2017 at 11:10 | history | edited | Zen | CC BY-SA 3.0 |
added 7 characters in body
|
| Sep 25, 2017 at 11:08 | history | asked | Ashok | CC BY-SA 3.0 |