Well... On Fri, Mar 22, 2013 at 8:20 AM, Ranjan Maitra < maitra.mbox.igno...@inbox.com> wrote:
> I don't believe that you necessarily need to use simulation for this. > But you do need numerical integration. Here is a skeletal approach. > > Calculate the density (distribution) of the order statistics of a > multivariate sample. Therein lies the difficulty. Try it for the non-iid case. Cheers, Bert > Then since the underlying distribution is > multivariate normal, use a multivariate integration routine in R (try > the mnormt package) to get the integration part of the calculation and > proceed. > > As I said before, here is the outline of an approach I would first take. > You get to work through the details:-) > > Ranjan > > > > > On Fri, 22 Mar 2013 10:48:06 -0400 li li <hannah....@gmail.com> wrote: > > > 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. > > > > > -- > Important Notice: This mailbox is ignored: e-mails are set to be > deleted on receipt. 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