Re: Integral of a bivariate function

*To*: mathgroup at smc.vnet.net*Subject*: [mg48784] Re: Integral of a bivariate function*From*: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>*Date*: Wed, 16 Jun 2004 04:54:57 -0400 (EDT)*References*: <cadvmq$6mf$1@smc.vnet.net> <cagij5$i9n$1@smc.vnet.net> <cam6de$qja$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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 hotmail.com> wrote in message news:cam6de$qja$1 at smc.vnet.net... > Many thanks for your reply Steve. Do you know if it is possible to get > an upper bound on the approximation error of this method in the > general case? For example if one is only interested in upper > p-quantiles of the distribution for small p. > > > > "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk> wrote in message news:<cagij5$i9n$1 at smc.vnet.net>... > > "Marc" <omid_rezayi at hotmail.com> wrote in message > > news:cadvmq$6mf$1 at smc.vnet.net... > > > 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