Inverse Mill's Ratio

[Yasuhiro Ohta]

Hi,

I am wondering whether someone is working on Inverse Mill's Ratio,
which is also known as the hazard function $\lambda(x)$:
\[
\lambda(x) = \frac{\phi(x)}{1-\Phi(x)},
\]
where $\phi(x)$ is the standard normal pdf, and $\Phi(x)$ is the
standard normal cdf.

Since this function behaves badly, a special treatment seems to be
needed.  I noticed the following paper:

Harold Ruben, "A New Asymptotic Expansion for the Normal Probability
Integral and Mill's Ratio," Journal of the Royal Statistical
Society. Series B (Methodological), Vol. 24, No. 1. (1962),
pp. 177-179.

This method might be able to be implemented.

Yasuhiro Ohta