R help - Mar 2009 - multivariate integration and partial differentiation

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


      
	[[alternative HTML version deleted]]

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


      
	[[alternative HTML version deleted]]

The adapt package has multivariate integration.

However, I am not sure you need the multivariate integration for the
example you describe: you only need one dimensional integration.  For
this, you can check out

?integrate

For differentiation, depending on how well behaved the cdf is, you
could use ?diff to calculate approximations for the slope.

HTH

Andrew

On Mar 7, 5:08?pm, Wei-han Liu <weihanliu2... at yahoo.com>
wrote:
> 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
>
> ? ? ? ? [[alternative HTML version deleted]]
>
> ______________________________________________
> R-h... at r-project.org mailing
listhttps://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

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


      
	[[alternative HTML version deleted]]

Hi,

The "adapt" package might work, but note that it cannot handle
infinite limits.  So, integrate() is your best bet.  Since you need to integrate
out only one dimension, integrate() would work just fine.

As for differentiation, you might try the grad() fucntion in the
"numDeriv" package.

Ravi.

____________________________________________________________________

Ravi Varadhan, Ph.D.
Assistant Professor,
Division of Geriatric Medicine and Gerontology
School of Medicine
Johns Hopkins University

Ph. (410) 502-2619
email: rvaradhan at jhmi.edu


----- Original Message -----
From: Wei-han Liu <weihanliu2002 at yahoo.com>
Date: Saturday, March 7, 2009 9:38 am
Subject: [R] multivariate integration and partial differentiation
To: r-help at r-project.org

> 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
>  
>  
>        
>  	[[alternative HTML version deleted]]
>  
>  ______________________________________________
>  R-help at r-project.org mailing list
>  
>  PLEASE do read the posting guide 
>  and provide commented, minimal, self-contained, reproducible code.