FAQ
In general, any n-th order partial derivative can be approximated by forming
the appropriate tensor product of n univariate approximations. If each
univariate approximation is based on a two-point central difference (which
involves 2 function evaluations), then the total number of function
evaluations in the tensor product is 2^n. So, if you have a bivariate
distribution, then its density is simply the second-order cross partial
derivative, which can be evaluated accurately with 4 function evaluations.
You can see that this problem quickly becomes non-trivial due to curse of
dimensionality.

Hope this helps.

Ravi.

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Division of Geriatric Medicine and Gerontology
Johns Hopkins University
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Email: rvaradhan at jhmi.edu
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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
bounces at stat.math.ethz.ch] On Behalf Of Cuvelier Etienne
Sent: Friday, May 06, 2005 3:03 AM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] Numerical Derivative / Numerical Differentiation of
unknownfunct ion
-----Original Message-----
From: Berton Gunter [mailto:gunter.berton at gene.com]
Sent: 05 May 2005 23:34
To: 'Uzuner, Tolga'; r-help at stat.math.ethz.ch
Subject: RE: [R] Numerical Derivative / Numerical Differentiation of
unknown funct ion

But...

See ?numericDeriv which already does it via a C call and hence is much
faster (and probably more accurate,too).
Is there is a similar function to calculate the numerical value of the
density of a given
multivariable distribution?
I have a function of a distribution H(x1, ...,xn) (not one of the known
distributions),
i.e. I can calculate a value of H for any (x1..., xn) .
And I want to calculate h(x1...,xn) for any (x1...,xn) BUT I don't know
the
analytical
expression of the density H.

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