Re: [R] Using integrate (was Discontinuities in a simple graph (machine precision?))

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From: Prof Brian Ripley (ripley@stats.ox.ac.uk)
Date: Wed 05 May 2004 - 19:35:25 EST


Message-id: <Pine.LNX.4.44.0405051023390.11754-100000@gannet.stats>

Note, this is about integrate, nothing else. You are looking for an
answer with high absolute precision for larger a because of your divisor
(about 1e-3). If I add rel.tol=1e-12 it is fine.

On Wed, 5 May 2004, Simon Cullen wrote:

> Hi,
>
> I've got an ugly but fairly simple function:
>
> mdevstdev <- function(a){
> l <- dnorm(a)/(1-pnorm(a))
> integrand <- function(z)(abs(z-l)*dnorm(z))
> inted <- integrate(integrand, a, Inf)
> inted[[1]]/((1- pnorm(a))*sqrt((1 + a*l - l^2)))
> }
>
> I wanted to quickly produce a graph of this over the range [-3,3] so I
> used:
>
> plotit <-function(x=seq(-3,3,0.01),...){
> y<-sapply(x,mdevstdev)
> plot(x,y,...)
> }
>
> > plotit()
>
> This produces the graph, but some discontinuities appear on it. I've
> produced the same graph in Mathematica 5
> (http://econserv2.bess.tcd.ie/cullens/R/DOverDelta.eps), and it was smooth
> over this range (it takes ages to run, though). Is this a numerical
> precision problem? Any suggestions on how to improve the precision?
>
> I'm running R 1.9 on WinXP, PIII. I haven't changed any R parameters that
> I know of.
>
>

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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