Re: [R] pnorm, relative accuracy in the tails

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From: Achim Zeileis (zeileis@ci.tuwien.ac.at)
Date: Thu 14 Feb 2002 - 02:51:37 EST 

Message-id: <3C6A8B89.A9BB9764@ci.tuwien.ac.at>

Ole Christensen wrote:
>
> Dear R people
>
> The function below should be decreasing, convex, and tend to zero when x
> tends to infinity.
>
> curve((1-pnorm(x))/dnorm(x),from=0, to=9)
>
> >From the plot we see that for x between 8.0 and 8.3 the function is
> fluctuating.

You get a numerically more stable result by using logs:

R> curve(exp(pnorm(x, lower.tail=FALSE, log.p=TRUE)-dnorm(x,
log=TRUE)),from=0, to=9)

> As far as I understand, this is due to the function pnorm() not being
> sufficiently accurate in the tails.
> I am using pnorm() in a way that has probably not been intended.
> So I guess this should not be considered a bug (??)
>
> The function can also be written as 1/lambda(x) where lambda(x) is the
> hazard rate for the normal distribution. Is there a way to calculate
> lambda(x) without using pnorm() ?
>
> Any help would be appreciated.
>
> Cheers
>
> Ole Christensen
>
> --
> Ole F. Christensen
> Department of Mathematics and Statistics
> Fylde College, Lancaster University
> Lancaster, LA1 4YF, England
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