Article 1ZYP4 Normal hazard continued fraction

Normal hazard continued fraction

by
John
from John D. Cook on (#1ZYP4)

The hazard function of a probability distribution is the instantaneous probability density of an event given that it hasn't happened yet. This works out to be the ratio of the PDF (probability density function) to the CCDF (complementary cumulative density function).

For the standard normal distribution, the hazard function is

normal_hazard.png

and has a surprisingly simple continued fraction representation:

normal_hazard_continued_fraction2.png

Aside from being an elegant curiosity, this gives an efficient way to compute the hazard function for large x. (It's valid for any positive x, but most efficient for large x.)

Source: A&S equation 26.2.14

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