Thank you!
    Hanna

2013/3/22 Ranjan Maitra <maitra.mbox.ignored@inbox.com>

> 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. 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.hlx@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.berton@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.Harding@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.Harding@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>
> <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
> > >
> > >
> >
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> >
> > ______________________________________________
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> >
>
>
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