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After searching for a while, I wonder if a continued fraction representation exists for the multivariate Mills ratio $P(Z \geq x)/\phi_Z(x)$ where $Z \tilde\, N(\mu,\Sigma)$. The representation should, of course, be in terms of $x$, $\mu$, and $\Sigma$.

Such a representation is well-known if $Z \tilde\, N(0,1)$; see, for example,

C-I. C. Lee., On Laplace continued fraction for the normal integral, Ann. Inst. Statist. Math., 44(1):107–120, March 1992.

(The same question is posted on stats stackexchange, see here)

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Also asked on stats.SE? stats.stackexchange.com/q/35006/6633 –  Dilip Sarwate Aug 24 '12 at 21:34
    
Indeed, I followed someone's suggestion by posting the question here. I have added links in each direction to avoid duplication of effort. –  Alexander Aug 25 '12 at 7:42
    
Cross-posting is not encouraged. Please choose one site and let moderators coordinate migration for you. –  chl Aug 25 '12 at 8:09

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