To: Philippe Lambert <phlamber@luc.ac.be> Subject: Re: R-beta: Quantile function From: Peter Dalgaard BSA <p.dalgaard@biostat.ku.dk> Date: 12 Feb 1998 13:42:03 +0100 In-Reply-To: Philippe Lambert's message of Thu, 12 Feb 1998 13:08:37 +0100 (MET) Philippe Lambert <phlamber@luc.ac.be> writes: > > Is the following behaviour of the quantile function what one would expect? > > a <- 1:100 > > quantile(a,.6) > 60% > 60.4 Yes... And so is > quantile(1:10) 0% 25% 50% 75% 100% 1.00 3.25 5.50 7.75 10.00 (Note that *three* values, 8,9,10 fall above the 75% quantile!) There are many possible definition of quantiles. R's (and Splus's) is to put 0% at the minimum and 100% at the maximum, and in general, the k-th smallest is at (k-1)/(n-1), with linear interpolation between the points. (Try plot(quantile(rnorm(5),seq(0,1,.01))) to see it). This can surely be criticized, e.g. you'll always have 1 observation below the 0.00..001 quantile! Alternatives might for example use (k-.5)/n which puts the smallest observation at 1/2n, but then it's tricky to define quantiles outside (1/2n,1-1/2n). -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._