Timeline for About Trivariate Normal Distribution
Current License: CC BY-SA 3.0
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| Sep 8, 2013 at 9:21 | comment | added | Glen_b | Oh, that's a very different problem to the one you posted about; here you're also dealing with the fact that the parameter estimates of $\mu$ and $\Sigma$ are not the same as the population quantities, but are themselves random variables. No hint of this problem is present in the original question. You might like to post a new question discussing the issue you have here. | |
| Sep 8, 2013 at 9:14 | comment | added | user29976 | Ok. This is the problem. I have three variables (say X,Y and Z) and their measurements from sample (X=[x1,x2,...xn],Y=[y1,y2,...yn],Z=[z1,z2,...zn]). On the basis of those measurements I want to define 95% confidence ellipsoid (in X,Y,Z coordinate space), so that I can infer that 95% of whole population (from which I took my sample) will fit in that ellipsoid. | |
| Sep 7, 2013 at 23:48 | comment | added | Glen_b | I'm sorry I didn't quite follow your explanation there. Could you clarify either your explanation of what you did or rephrase your question more precisely into a form that doesn't require an explanation of what you did at all? | |
| Sep 7, 2013 at 19:14 | comment | added | user29976 | We got 95% confidence ellipsoid for 3 principal components by PCA on the first sample, and wanted to check it with next smaller sample and got the result that 72% of cases are found inside of ellipsoid. Are we right that explanation lies in the fact that ellipsoid contains 72% of the probability of the trivariate normal distribution? | |
| Sep 6, 2013 at 11:35 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 6, 2013 at 9:51 | history | edited | Glen_b | CC BY-SA 3.0 |
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| Sep 6, 2013 at 9:41 | history | answered | Glen_b | CC BY-SA 3.0 |