Yes. What I meant is "the distribution of order statistics from a non-iid sample of a (normal) distribution with specified sample covariance matrix". Thanks for the idea of simulation. I guess there is no other way around. Hanna
2013/3/22 Bert Gunter <gunter.ber...@gene.com> > As you suggest, Ted, it appears from the question that the OP really means > "order statistics of a sample of 10 from the distribution." So what she > appears to want is the distribution of order statistics from a non-iid > sample of a (normal) distribution with specified sample covariance matrix. > > The independent case is standard first statistics course stuff, but I > believe this would require a 10-d integral (please correct if wrong!) for > non-iid. So it would seem that simulation would be the simplest approach, > and, indeed, should be straightforward. E.g. the mvrnorm() function in MASS > could be used to simulate the samples. > > Again, corrections appreciated if I am wrong on any of this. > > -- Bert > > > > On Fri, Mar 22, 2013 at 6:31 AM, Ted Harding <ted.hard...@wlandres.net>wrote: > >> On 22-Mar-2013 13:02:25 li li wrote: >> > Thank you all for the reply. >> > >> > One example of my question is as follows. >> > >> > Suppose X1, ..., X10 has multivariate normal distribution >> > and X(1), ..., X(10) are the corresponding order statistics. >> > >> > My question is that whether there is a R function that would >> > help compute the c which satisfies >> > P(X(4) <c)=beta. >> > Here beta is a known constant between 0 and 1. >> > >> > Thank you. >> > Hanna >> >> The basic question which needs to be answered (which has been hinted >> at in earlier replis) is: How do you define "order statistic" for >> multivariate observations? >> >> For example, here is a sample of 10 (to 3 d.p.) from a bivariate >> normal distribution: >> >> [,1] [,2] >> [1,] 1.143 -0.396 >> [2,] -0.359 -0.217 >> [3,] -0.391 -0.601 >> [4,] -0.416 -1.093 >> [5,] -1.810 -1.499 >> [6,] -0.367 -0.636 >> [7,] -2.238 0.563 >> [8,] 0.811 1.230 >> [9,] 0.082 0.174 >> [10,] -1.359 -0.364 >> >> Which one of these 10 rows is X(4)? >> >> There is an alternative interpretation of your question: >> >> "Suppose X1, ..., X10 has multivariate normal distribution >> and X(1), ..., X(10) are the corresponding order statistics." >> >> This could mean that the vector (X1,...,X10) has a multivariate >> normal distribution with 10 dimensions, and, for a single vector >> (X1,...,X10) drawn from this distribution, (X(1), ..., X(10)) >> is a vector consisting of these same values (X1,...,X10), but >> in increasing order. >> >> Is that what you mean? >> >> Hoping this helps, >> Ted. >> >> >> ------------------------------------------------- >> E-Mail: (Ted Harding) <ted.hard...@wlandres.net> >> Date: 22-Mar-2013 Time: 13:31:31 >> 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<http://www.r-project.org/posting-guide.html> >> and provide commented, minimal, self-contained, reproducible code. >> > > > > -- > > Bert Gunter > Genentech Nonclinical Biostatistics > > Internal Contact Info: > Phone: 467-7374 > Website: > > http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm > > [[alternative HTML version deleted]] ______________________________________________ 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.