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Re: Integral of a bivariate function

  • To: mathgroup at
  • Subject: [mg48784] Re: Integral of a bivariate function
  • From: "Steve Luttrell" <steve_usenet at>
  • Date: Wed, 16 Jun 2004 04:54:57 -0400 (EDT)
  • References: <cadvmq$6mf$> <cagij5$i9n$> <cam6de$qja$>
  • Sender: owner-wri-mathgroup at

I can't see a rigorous answer to your question. The error depends on too
many uncontrolled things in the general case. I must confess that I simply
wrote down my original suggestion (the Mathematica notebook) off the top of
my head, so it was intended only to be a quick-and-dirty numerical solution
to the problem.

Steve Luttrell

"Marc" <omid_rezayi at> wrote in message
news:cam6de$qja$1 at
> Many thanks for your reply Steve. Do you know if it is possible to get
> an upper bound on the approximation error of this method in the
> general case? For example if one is only interested in upper
> p-quantiles of the distribution for small p.
> "Steve Luttrell" <steve_usenet at> wrote in
message news:<cagij5$i9n$1 at>...
> > "Marc" <omid_rezayi at> wrote in message
> > news:cadvmq$6mf$1 at
> > > For a given bivariate function I want  to calculate the integral of
> > > the function over an arbitrary compact region A, for instance over
> > > A={(x,y)| f(x,y)=c} for some constant c. The function is smooth and in
> > > my application it is the joint density of two continuous random
> > > variables. I wonder if this can be done in Mathematica and in that
> > > case how. Otherwise I'd appreciate any pointer to other programs which
> > > can be used for this.
> > >
> >
> > Here is a notebook that describes how I would solve this problem. Select
> > from the first (*** to the last ****) and copy/paste anywhere in
> > Mathematica; it will automatically detect that you are pasting a whole
> > notebook.
> >
> > Steve Luttrell
> >

....notebook snipped

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