>>>>> "Matthias" == Matthias Kohl <[EMAIL PROTECTED]> >>>>> on Thu, 15 Jan 2004 13:55:22 +0000 writes:
Matthias> Hello, by checking the precision of a convolution Matthias> algorithm, we found the following "inexactness": Matthias> We work with R Version 1.8.1 (2003-11-21) on Matthias> Windows systems (NT, 2000, XP). Matthias> Try the code: Matthias> So for lambda=977.8 and x=1001 we get a distance Matthias> of about 5.2e-06. (This inexactness seems to hold Matthias> for all lambda values greater than about 900.) Matthias> BUT, summing about 1000 terms of exactness around 1e-16, Matthias> we would expect an error of order 1e-13. Matthias> We suspect algorithm AS 239 to cause that flaw. correct. Namely, because ppois(x, lambda, lower_tail, log_p) := pgamma(lambda, x + 1, 1., !lower_tail, log_p) and pgamma(x, alph, scale) uses AS 239, currently. So this thread is really about the precision of R's current pgamma(). In your example, (x = 977.8, alph = 1002, scale=1) and in pgamma.c, alphlimit = 1000; and later /* use a normal approximation if alph > alphlimit */ if (alph > alphlimit) { pn1 = sqrt(alph) * 3. * (pow(x/alph, 1./3.) + 1. / (9. * alph) - 1.); return pnorm(pn1, 0., 1., lower_tail, log_p); } So, we could conceivably improve the situation by increasing `alphlimit'. Though, I don't see a real need for this (and it will cost CPU cycles in these cases). Matthias> Do you think this could cause other problems apart Matthias> from that admittedly extreme example? no, I don't think. Look at > lam <- 977.8 > (p1 <- ppois(1001, lam)) [1] 0.77643705 > (p2 <- sum(dpois(0:1001, lam))) [1] 0.77643187 Can you imagine a situation where this difference matters? Matthias> Thanks for your attention! You're welcome. Martin Maechler <[EMAIL PROTECTED]> http://stat.ethz.ch/~maechler/ Seminar fuer Statistik, ETH-Zentrum LEO C16 Leonhardstr. 27 ETH (Federal Inst. Technology) 8092 Zurich SWITZERLAND phone: x-41-1-632-3408 fax: ...-1228 <>< ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html