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
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