approximation to ln \Phi(x)

classic Classic list List threaded Threaded
2 messages Options
Reply | Threaded
Open this post in threaded view
|

approximation to ln \Phi(x)

richarddmorey
I am using pnorm() with the log.p=T argument to get approximations to ln \Phi(x) and qnorm with the log.p=T argument to get estimates of \Phi^{-1}(exp(x)). What approximations are used in these two functions (I noticed in the source pnorm.c it doesn't look like Abramowitz and Stegen) and where can I find the citation?

Thanks,
Richard Morey

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
Reply | Threaded
Open this post in threaded view
|

Re: approximation to ln \Phi(x)

Brian Ripley
On Tue, 31 Jan 2006, Morey, Richard D (UMC-Student) wrote:

> I am using pnorm() with the log.p=T argument to get approximations to ln
> \Phi(x) and qnorm with the log.p=T argument to get estimates of
> \Phi^{-1}(exp(x)). What approximations are used in these two functions
> (I noticed in the source pnorm.c it doesn't look like Abramowitz and
> Stegen) and where can I find the citation?

?qnorm says

      'qnorm' is based on Wichura's algorithm AS 241 which provides
      precise results up to about 16 digits.

You can also see this at src/nmath/qnorm.c in the sources.

For pnorm.c, the comments describe the origins of the main approximation.

There are other distribution function approximations in R which are based
on undocumented ideas, but these are fairly well documented, especially
qnorm.

--
Brian D. Ripley,                  [hidden email]
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html