Question: Let be the survivor function of a standard normal random variable. As in Smith (2004, p. 12), show that, for k > 0, This result

Let be the survivor function of a standard normal random variable. As in Smith (2004, p. 12), show that, for k > 0,

lim x+x (x+k/x) $(x) e-k

This result arises in the study of extreme value theory (see Smith (2004) and Coles (2001) for detailed, accessible accounts).

lim x+x (x+k/x) $(x) e-k

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