# $\chi^2$ distance and multivariate gaussian distribution

I want to know how to write the $\chi^{2}$ distance between two multivariate Gaussian distributions $f$ and $g$ in terms of their parameters only. The parameters of $f$ is the vector $\mu_{1}$ and a covariance matrix $\Sigma_{1}$. The parameters of $g$ is the vector $\mu_{2}$ and a covariance matrix $\Sigma_{2}$.

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I would think that distance would be a measure of the separation of the mean vectors.  But that would require a common scale.  If the covariance matrices were equal I would think the Mahalanobis distance might be what the OP is referring to. – Michael Chernick Aug 4 '12 at 14:30
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