Message-ID: <Pine.GSO.4.10.10203071217270.18194-100000@quetelet.stat.ucla.edu>
Date: 2002-03-07T20:17:55Z
From: Roger D. Peng
Subject: integrate function
In-Reply-To: <5.1.0.14.0.20020307144125.00a768c0@ctfs.si.edu>
I'm curious to see which methods you tried. I too am looking for a decent
numerical integration routine.
-roger
_______________________________
UCLA Department of Statistics
rpeng at stat.ucla.edu
http://www.stat.ucla.edu/~rpeng
On Thu, 7 Mar 2002, Richard Condit wrote:
> After finding an error in R's integrate function, I spent some time testing
> various alternative numerical integration routines I took from the
> Numerical Recipes book by Press et al. Here is a brief summary of what I found.
>
> As near as I can tell, no method for numerical integration is foolproof. I
> believe that no matter the method, functions could be invented to defeat
> it. In particular, as Ole Christensen pointed out, if a function has
> positive values only in a very narrow range, then numerical routines cannot
> be guaranteed to find it.
>
> R's integrate function works better more often than the alternatives I
> tested. It succeeded with some very tricky functions that foiled the other
> methods. But it did fail in some circumstances.
>
> My only advice about the R integrate function would be to point out in
> documentation that the value returned as "abs error" is not in fact the
> error. There is no way I found of calculating the deviation between a
> numerical estimate of an integral and the true integral. Abs error is
> simply the change in the estimate between the last 2 iterations of the
> numerical routine. In many cases, this should be a rough approximation of
> the discrepancy between estimate and true integral, but if integrate fails,
> abs error fails too. I would suggest abs error not even be returned with
> the estimate of the integral, since it doesn't add information (since
> abs.tol is set in the function).
>
> I can provide more information about the various methods and their errors,
> if anyone is interested.
>
>
> Rick
>
>
>
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