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Q112Section III (Statistics)112 of 145

The Mahalanobis form of Xˉ\bar X is χp2\chi^2_p

If X‾∼Np(μ‾,Σ)\underline X\sim N_p(\underline\mu,\Sigma), then the distribution of N(X‾ˉ−μ‾)′Σ−1(X‾ˉ−μ‾)N(\bar{\underline X}-\underline\mu)'\Sigma^{-1}(\bar{\underline X}-\underline\mu) would be:

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