Hi Ted > -----Original Message----- > From: ted@deb [mailto:ted@deb] On Behalf Of Ted Harding > Sent: Tuesday, October 30, 2012 6:41 PM > To: r-help@r-project.org
<snip> > > The general asymptotic result for the pth quantile (0<p<1) X.p of a > sample of size n is that it is asymptotically Normally distributed with > mean the pth quantile Q.p of the parent distribution and > > var(X.p) = p*(1-p)/(n*f(Q.p)^2) > > where f(x) is the probability density function of the parent > distribution. So if I understand correctly p*(1-p) is biggest when p=0.5 and decreases with smaller or bigger p. The var(X.p) then depends on ratio to parent distribution at this p probability. For lognorm distribution and 200 values the resulting var is > (0.5*(1-.5))/(200*qlnorm(.5, log(200), log(2))^2) [1] 3.125e-08 > (0.1*(1-.1))/(200*qlnorm(.1, log(200), log(2))^2) [1] 6.648497e-08 so 0.1 var is slightly bigger than 0.5 var. For different distributions this can be reversed as Jim pointed out. Did I manage to understand? Thank you very much. Regards Petr > > This is not necessarily very helpful for small sample sizes (depending > on the parent distribution). > > However, it is possible to obtain a general result giving an exact > confidence interval for Q.p given the entire ordered sample, though > there is only a restricted set of confidence levels to which it > applies. > > If you'd like more detail about the above, I could write up derivations > and make the write-up available. > > Hoping this helps, > Ted. > > ------------------------------------------------- > E-Mail: (Ted Harding) <ted.hard...@wlandres.net> > Date: 30-Oct-2012 Time: 17:40:55 > This message was sent by XFMail > ------------------------------------------------- ______________________________________________ R-help@r-project.org 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.
