> pbinom(1, 2, .5)
[1] 0.75
This is the binomial cumulative distribution function.
*** pbinom(0, 2, .5) = 0.25
*** pbinom(1, 2, .5) = 0.75 = 0.25 + 0.5
*** pbinom(2, 2, .5) = 1
However, pbinom(1e15, 2e15, .5) is a computational challenge. Standard numerical algorithms often fail in situations like this. The code should test for such cases and use more numerically stable "approximations" in place of the "exact" algorithms.
The standard deviation for a binomial is sqrt(p*(1-p)/n) = 0.5/sqrt(2e15), which is roughly 1e-8 in your case.
I get the following from both S-Plus and R:
> pbinom(1e5+c(-1, 0, 1), 2e5, .5)
[1] 0.4991079 0.5008921 0.5026762
For the problem you cite, the correct answer should be 0.5 to about 8 significant digits. Instead, I get 1 from R (as you did) and the following from S-Plus:
> pbinom(1e15,2e15,0.5)
[1] 0.7411209
Both give wrong answers without warning, though in this case, S-Plus is closer.
Answer the question?
Spencer Graves
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[EMAIL PROTECTED] wrote:
Dear all Just for fun, I have just downloaded the paper mentioned below and checked it with R-1.6.1. Everything is ok with exception of Table 2b, where I get always 1 instead of 0.5:pbinom(1e15,2e15,0.5)[1] 1 Which value should be correct? Best regards Christian Stratowa ============================================== Christian Stratowa, PhD Boehringer Ingelheim Austria Dept NCE Lead Discovery - Bioinformatics Dr. Boehringergasse 5-11 A-1121 Vienna, Austria Tel.: ++43-1-80105-2470 Fax: ++43-1-80105-2683 email: [EMAIL PROTECTED]-------- Original Message -------- Subject: Re: [S] Exact p-values Date: Thu, 13 Feb 2003 18:31:38 +0100 From: "Rau, Roland" <[EMAIL PROTECTED]> To: 'Spencer Graves' <[EMAIL PROTECTED]>, Jose Mar�a Fedriani Laffitte <[EMAIL PROTECTED]> CC: [EMAIL PROTECTED] Dear all, in relation to your question, the following working paper of Leo Knuesel, University of Munich, might be of interest: "On the Accuracy of Statistical Distributions in S-Plus for Windows (1999)" You can download the paper from (pdf-Format, 45k): http://www.stat.uni-muenchen.de/~knuesel/elv/accuracy.html Best, Roland > -----Original Message----- > From: Spencer Graves [SMTP:[EMAIL PROTECTED]] > Sent: Thursday, February 13, 2003 6:12 PM > To: Jose Mar�a Fedriani Laffitte > Cc: [EMAIL PROTECTED] > Subject: Re: [S] Exact p-values > > > Try ( 1-pchisq(29.8, df=1)): With S-Plus 6.1, I got 4.78992e-008. > > By the way, the distribtion functions in R have more arguments. > For example, pchisq(29.8, df=1, lower.tail=F) produces the same > answer, and pchisq(29.8, df=1, lower.tail=F, log=T) produces its natural > logarithm. Also, pchisq, dchisq, qchisq, and rchisq in R all have an > "ncp" noncentrality parameter argument; only pchisq has such in S-Plus > 6.1. Similarly, none of the Student's t functions in S-Plus have a > non-centralitity parameter; in R, pt has an argument ncp, and from this > one can easily program ncp for dt, qt and rt. Also, the distribution > functions in the current release of S-Plus are known to have problems. > For example, pt(-1, Inf) = 0.5 in S-Plus 6.1, but 0.159 in R; clearly, > S-Plus gives a wrong answer without warning. > > Best Wishes, > Spencer Graves > > Jose Mar�a Fedriani Laffitte wrote: > > >Dear all, > > > > I want to get the exact p-values, on 1 degree of freedom, for an > array > >of chi-square values. When my chi-square values are equal or lower than > >29.7, I get the exact associated p-values. Thus, for instance: > > > > > > > >>pchisq(29.7, df=1) > >> > >> > >[1] 0.9999999 > > > >However, when my chi-square values are greater or equal to 29.8 what I > get > >is: > > > > > > > >>pchisq(29.8, df=1) > >> > >> > >[1] 1 > > > > > > Could anyone tell me how to fix this trivial issue? Very grateful, > Jose > >M. Fedriani > > > >**************************************** > >Jose M� Fedriani Laffitte > >Estacion Biologica de Donana (CSIC) > >Avda. M� Luisa s/n > >41013-Sevilla > >Spain > >Tel. +34-954232340 > >Fax +34-954621125 > >http://ebd.csic.es > > > >-------------------------------------------------------------------- > >This message was distributed by [EMAIL PROTECTED] To > >...(s-news-request clipped)...> > > > > > > -------------------------------------------------------------------- > This message was distributed by [EMAIL PROTECTED] To > ...(s-news-request clipped)...-------------------------------------------------------------------- This message was distributed by [EMAIL PROTECTED] To ...(s-news-request clipped)...______________________________________________ [EMAIL PROTECTED] mailing list http://www.stat.math.ethz.ch/mailman/listinfo/r-help
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