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
>>
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>> PLEASE do read the posting guide
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>
>
>
> --
>
> 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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