Respected R Users,

I looking for help with generating theoretical confidence regions for any
of non-symmetric bivariate statistical distributions (bivariate Chi-squared
distribution<Wishart distribution>, bivariate F-distribution, or any of the
others). I want to to used it as a benchmark to compare a few strategies
constructing confidence regions for non-symmetric bivariate data.

There is a paper proposed an accumulative function for bivaraite
F-Distribution, but it was basically oriented for "one-tail" testing. I
understand that it is nonsense to consider two-tails of F or Chi^2
distribution in most cases. But we may still need to know the confidence
intervals of a estimate following the distributions in some situations.
Thereby, please forget the necessity of the question itself.  In one word,
my question is: for two variables x and y, which are following chi^2
distributions (df=4), independently, what is the theoretical confidence
region of the joint distribution of x,y for a given alpha? Since the issues
has already beyond my research area, please let me know if my descriptions
are confusing. Numeric strategies are also welcomed for the issue.

I appropriate your kindly help with the matter.

Best regards,

Zhiqiu

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