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 > 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.
