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:

$N(\mu_1,\Sigma), N(\mu_2,\Sigma), N(\mu_3,\Sigma)...$

  • $\begingroup$ Do you mean with the same variances and with all covariances between pairs of different variables the same? $\endgroup$
    – Glen_b
    Mar 17, 2016 at 2:32
  • $\begingroup$ @Glen_b yes, all the same, the only difference is the mean. $\endgroup$
    – dontloo
    Mar 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_b
    Mar 17, 2016 at 2:40
  • $\begingroup$ @Glen_b sorry I misunderstood, yes $\Sigma$ is just an arbitrary covariance matrix. $\endgroup$
    – dontloo
    Mar 17, 2016 at 2:42

1 Answer 1


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.


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