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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 $\Sigma_{2}$.

gung - Reinstate Monica
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alya
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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 R. Chernick Aug 04 '12 at 14:30
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    That isn't the best choice of duplicate. This should be a duplicate of [What is the distribution of the euclidean distance between two normally distributed random variables](http://stats.stackexchange.com/q/9220/7290) instead. – gung - Reinstate Monica Dec 05 '15 at 15:50
  • @gung: agreed; let's close this 33666 and that 30218 as duplicates of the older 9220. – Felipe G. Nievinski Dec 05 '15 at 18:54

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