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I am trying to solve what the Survival function for a std. normal, so $1-\Phi(z) = P(Z>z)$, converges to as $\lim_{z \to +\infty}$. I think this may involve the error function but I'm getting stuck trying to simplify the expression.

I know it will involve something like ( $\frac{\phi(z)}{z}$ ) but I'm not sure. Any help is much appreciated :)

RaphaelKnecht
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    See the discussion of Mills' ratio for example [here](https://stats.stackexchange.com/a/7206/805) and [here](https://mathoverflow.net/questions/330054/bounds-on-the-mills-ratio) .... more terms in the asymptotic expansion can be figured out from the information [here](https://bowaggoner.com/blog/2018/03-17-gaussian-tails/index.html). or as given [here](https://www.sciencedirect.com/science/article/pii/S0022247X14004764) – Glen_b Sep 30 '20 at 05:55
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    Do you mean "complement" or "complementary" rather than "inverse" for $(1-\Phi(x))$? – Xi'an Sep 30 '20 at 08:57
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    Could you clarify what you mean by "inverse of"? Would that be the *functional inverse* or would it be the *reciprocal* or maybe something else? – whuber Sep 30 '20 at 14:37

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