[R-SIG-Finance] multivariate integration and partial differentiation

[Krishna Kumar]

Wei-han Liu wrote:
> Hi R Users:
>
> Could somebody share some tips on implementing multivariate integration and partial differentiation in R? 
> For example, for a trivariate joint distribution (cumulative density function) of F(x,y,z), how to differentiate with respect to x and get the bivariate distribution (probability density function) of f(y,z). Or integrate f(x,y,z) with respect to x to get bivariate distribution of (y,z).
> Your sharing is appreciated.
> Wei-han Liu
>
>
>       
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Hi there are several multivariate integration possibilities in R besides 
Pseudo-MC/Quasi-MC, R package adapt that does adaptive quadrature
based on fortran code from Alan Genz. There is also a package that does 
sparse grids (what is also goes as Smolyak Construction) but I can't 
seem to locate it quickly.

In order to compute the cumulative distribution have a look at package 
mvtnorm, also it is possible to interface to mulnor directly from R 
using Rcpp or simillar.

Best
Krishna