CODEWITHSUNDEEP
rstatisticsnormal-distributionprobability-density
drawar
drawar

Reputation: 243

Quantile of a bivariate normal/student-t distribution

I'm wondering if there's a function in R that is able to solve for x in the following equation
P(X < x, Y< a) = b,
where (X,Y) follows either a bivariate normal distribution or (skew) Student-t distribution and a and b are known.

In other words, I'm trying to compute the upper bound x of the double integral integral

Upvotes: 1

Views: 602

Answers (1)

Robert Dodier
Robert Dodier

Reputation: 17575

Well, as the problem is stated, this is a 1-dimensional root-finding problem. (That's good news.)

When the pdf is a Gaussian pdf, I think you can compute the double integral symbolically (try a computer algebra system such as Maxima for that) but then you will have to apply a numerical root-finding function such as stats::uniroot in R.

When the pdf is a Student t or skewed Student t pdf, there is probably a symbolic solution for one dimensional integration but probably not for two. So the outer integral will probably have to be represented as a numerical function. You can apply a numerical root-finding function to your representation of the outer integral, as in the Gaussian case.

Upvotes: 1

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