Re: [R] pnorm how to decide lower-tail true or false
> "CM" == Carmen Meier <[EMAIL PROTECTED]>
> on Fri, 08 Jun 2007 19:31:49 +0200 writes:
CM> Hi to all, maybe the last question was not clear enough.
CM> I did not found any hints how to decide whether it
CM> should use lower.tail or not. As it is an extra
CM> R-feature ( written in
CM> http://finzi.psych.upenn.edu/R/Rhelp02a/archive/66250.html
CM> ) I do not find anything about it in any statistical
CM> books of me.
Yes, most "statistical books" do not consider numerical accuracy
which is the real issue here.
Note that R is much more than a "statistical package" and hence
to be appreciated properly needs much broader (applied)
mathematical, statistical and computer science knowledge ;-)
When p ~= 1, '1 - p' suffers from so called cancellation
("Numerical analysis 101").
If you already know that you will use "q := 1 - p",
rather compuate 'q' directly than first compute p, then 1-p,
losing all accuracy.
All of R's p(..) functions have an argument 'lower.tail'
which is TRUE by default, since after all,
p(x) = Prob_{}[X <= x]
measures the probability of the lower or left tail of the
-distribution.
= norm is just a special case.
If you really want
q = 1 - p(x) = Prob_{}[X > x]
then you can get this directly via
q <- p(x, lower.tail = FALSE, )
Simple example with R :
> pnorm(10)
[1] 1
> 1 - pnorm(10)
[1] 0
> pnorm(10, lower.tail=FALSE)
[1] 7.619853e-24
Regards,
Martin Maechler, ETH Zurich
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Re: [R] pnorm how to decide lower-tail true or false
At 01:31 PM 6/8/2007, Carmen wrote: >Hi to all, >maybe the last question was not clear enough. >I did not found any hints how to decide whether it should use lower.tail >or not. >As it is an extra R-feature ( written in >http://finzi.psych.upenn.edu/R/Rhelp02a/archive/66250.html ) >I do not find anything about it in any statistical books of me. >Regards Carmen pnorm(z, lower.tail=TRUE) (the R default) gives the probability of a normal variate being at or below z. This is the value commonly called the cumulative distribution function at the point z, or the integral from -Inf to z of the gaussian density. pnorm(z, lower.tail=FALSE) gives the complement of the above, or 1 - cdf(z), and is the integral from z to Inf of the gaussian density. E.g., > pnorm(1.96, lower.tail=TRUE) [1] 0.9750021 > pnorm(1.96, lower.tail=FALSE) [1] 0.02499790 > Use lower.tail=TRUE if you are, e.g., finding the probability at the lower tail of a confidence interval or if you want to the probability of values no larger than z. Use lower.tail=FALSE if you are, e.g., trying to calculate test value significance or at the upper confidence limit, or you want the probability of values z or larger. You should use pnorm(z, lower.tail=FALSE) instead of 1-pnorm(z) because the former returns a more accurate answer for large z. This is really simple issue, and has no inherent complexity associated with it. Robert A. LaBudde, PhD, PAS, Dpl. ACAFS e-mail: [EMAIL PROTECTED] Least Cost Formulations, Ltd.URL: http://lcfltd.com/ 824 Timberlake Drive Tel: 757-467-0954 Virginia Beach, VA 23464-3239Fax: 757-467-2947 "Vere scire est per causas scire" __ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
[R] pnorm how to decide lower-tail true or false
Hi to all, maybe the last question was not clear enough. I did not found any hints how to decide whether it should use lower.tail or not. As it is an extra R-feature ( written in http://finzi.psych.upenn.edu/R/Rhelp02a/archive/66250.html ) I do not find anything about it in any statistical books of me. Regards Carmen __ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
