RE: [R] Confidence Band for empirical distribution function
Dear Kjetil, As I already mentioned, it appears that there isn't a function available calculating the quantiles directly (at least, it doesn't appear in the C source of ctest). So as I already suggested, uniroot (or a similar C routine which calls the corresponding C code directly) is probably the best you can do (apart from writing it completely yourself). I didn't program this using uniroot, but I'd certainly try the following for speed-up: - For symmetry reasons, you only need to compute half of the quantiles. - The quantiles depend smoothly on the probabilities (of your reference distribution). Therefore, calculating only a few for probabilities between 0 and 0.5, and using (e.g. linear) interpolation should be satisfying. I am sorry not be of more help. HTH anyway Thomas -Original Message- From: kjetil brinchmann halvorsen [mailto:[EMAIL PROTECTED] Sent: 23 July 2003 15:46 To: Hotz, T. Subject: RE: [R] Confidence Band for empirical distribution function On 22 Jul 2003 at 11:37, Hotz, T. wrote: Dear Leif, If you look at the definition of ks.test, you'll find the lines pkstwo - function(x, tol = 1e-06) { if (is.numeric(x)) x - as.vector(x) else stop(Argument x must be numeric) p - rep(0, length(x)) p[is.na(x)] - NA IND - which(!is.na(x) (x 0)) if (length(IND) 0) { p[IND] - .C(pkstwo, as.integer(length(x)), p = as.double(x[IND]), as.double(tol), PACKAGE = ctest)$p } return(p) } which calls C code to calculate the p-values given the test statistic. You'll find explanations on what this function does in the original C file src/library/ctest/src/ks.c I haven't tried that but I assume that you could use it to calculate p-values given the test-statistics yourself. That could certainly be done, but what was asked for is the inverse, which can be calculated, using for instance uniroot(). I tried that, but it is to slow, .C() will be called repeatedly in a loop. For me it took several minutes. Kjetil Halvorsen Please also note that ks.test() returns the p-value as well. If you need quantiles, I assume you need to invert the cdf yourself, e.g. using uniroot(). HTH Thomas --- Thomas Hotz Research Associate in Medical Statistics University of Leicester United Kingdom Department of Epidemiology and Public Health 22-28 Princess Road West Leicester LE1 6TP Tel +44 116 252-5410 Fax +44 116 252-5423 Division of Medicine for the Elderly Department of Medicine The Glenfield Hospital Leicester LE3 9QP Tel +44 116 256-3643 Fax +44 116 232-2976 -Original Message- From: Leif.Boysen [mailto:[EMAIL PROTECTED] Sent: 21 July 2003 14:42 To: [EMAIL PROTECTED] Subject: [R] Confidence Band for empirical distribution function Hi, I was trying to draw an empirical distribution function with uniform confidence bands. So I tried to find a way to calculate values of the Kolmogorov-Smirnov Distribution but failed. I guess it must be hidden somewhere (since the ks-test is implemented), but I was unable to find it. Is there any way to do this? Thanks Leif Boysen __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
RE: [R] Confidence Band for empirical distribution function
On Thu, 24 Jul 2003, Hotz, T. wrote: Dear Kjetil, As I already mentioned, it appears that there isn't a function available calculating the quantiles directly (at least, it doesn't appear in the C source of ctest). So as I already suggested, uniroot (or a similar C routine which calls the corresponding C code directly) is probably the best you can do (apart from writing it completely yourself). I didn't program this using uniroot, but I'd certainly try the following for speed-up: - For symmetry reasons, you only need to compute half of the quantiles. - The quantiles depend smoothly on the probabilities (of your reference distribution). Therefore, calculating only a few for probabilities between 0 and 0.5, and using (e.g. linear) interpolation should be satisfying. There is an example of this in my package HyperbolicDist which has just appeared on CRAN. It is a little more sophisticated in that it fits a spline in preference to linear interpolation, before using uniroot. Look at qhyperb if this is of interest. David Scott _ David Scott Department of Statistics, Tamaki Campus The University of Auckland, PB 92019 AucklandNEW ZEALAND Phone: +64 9 373 7599 ext 86830 Fax: +64 9 373 7000 Email: [EMAIL PROTECTED] Graduate Officer, Department of Statistics Webmaster, New Zealand Statistical Association: http://www.stat.auckland.ac.nz/nzsa/ __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
RE: [R] Confidence Band for empirical distribution function
Dear Leif, If you look at the definition of ks.test, you'll find the lines pkstwo - function(x, tol = 1e-06) { if (is.numeric(x)) x - as.vector(x) else stop(Argument x must be numeric) p - rep(0, length(x)) p[is.na(x)] - NA IND - which(!is.na(x) (x 0)) if (length(IND) 0) { p[IND] - .C(pkstwo, as.integer(length(x)), p = as.double(x[IND]), as.double(tol), PACKAGE = ctest)$p } return(p) } which calls C code to calculate the p-values given the test statistic. You'll find explanations on what this function does in the original C file src/library/ctest/src/ks.c I haven't tried that but I assume that you could use it to calculate p-values given the test-statistics yourself. Please also note that ks.test() returns the p-value as well. If you need quantiles, I assume you need to invert the cdf yourself, e.g. using uniroot(). HTH Thomas --- Thomas Hotz Research Associate in Medical Statistics University of Leicester United Kingdom Department of Epidemiology and Public Health 22-28 Princess Road West Leicester LE1 6TP Tel +44 116 252-5410 Fax +44 116 252-5423 Division of Medicine for the Elderly Department of Medicine The Glenfield Hospital Leicester LE3 9QP Tel +44 116 256-3643 Fax +44 116 232-2976 -Original Message- From: Leif.Boysen [mailto:[EMAIL PROTECTED] Sent: 21 July 2003 14:42 To: [EMAIL PROTECTED] Subject: [R] Confidence Band for empirical distribution function Hi, I was trying to draw an empirical distribution function with uniform confidence bands. So I tried to find a way to calculate values of the Kolmogorov-Smirnov Distribution but failed. I guess it must be hidden somewhere (since the ks-test is implemented), but I was unable to find it. Is there any way to do this? Thanks Leif Boysen __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help __ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help