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Inverse Mill's Ratio
- From: Yasuhiro Ohta <yohta at yorku dot ca>
- To: gsl-discuss at sources dot redhat dot com
- Date: Sun, 06 Apr 2003 18:52:10 -0400 (EDT)
- Subject: Inverse Mill's Ratio
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