What do we call a set of Gaussian distributions with the same covariance but different means?
Is there a particular term for that?
I mean the Gaussians are like:
$N(\mu_1,\Sigma), N(\mu_2,\Sigma), N(\mu_3,\Sigma)...$
$\begingroup$
$\endgroup$
4
-
$\begingroup$ Do you mean with the same variances and with all covariances between pairs of different variables the same? $\endgroup$– Glen_bMar 17, 2016 at 2:32
-
$\begingroup$ @Glen_b yes, all the same, the only difference is the mean. $\endgroup$– dontlooMar 17, 2016 at 2:33
-
$\begingroup$ Wait, I thought you were talking about common values within a single $\Sigma$. So the common $\Sigma$ is an arbitrary covariance matrix? $\endgroup$– Glen_bMar 17, 2016 at 2:40
-
$\begingroup$ @Glen_b sorry I misunderstood, yes $\Sigma$ is just an arbitrary covariance matrix. $\endgroup$– dontlooMar 17, 2016 at 2:42
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
When different multivariate distributions have the same covariance matrix, you could describe them as having "common covariance structure" or "a common covariance matrix, $\Sigma$".
You could perhaps try a term like "equi-covariant" but I don't think I've seen such a term used, and it might not be understood.
