[R] puzzle with integrate over infinite range

[Matt Shotwell]

You could try pnorm also:

shiftedGaussR <- function(x0 = 500) {
    sd  <- 100/sqrt(2)
    int <- pnorm(0, x0, sd, lower.tail=FALSE, log.p=TRUE)
    exp(int + log(sd) + 0.5 * log(2*pi))
}

> shiftedGaussR(500)
[1] 177.2454
> shiftedGauss(500)
[1] 177.2454

-Matt


On Tue, 2010-09-21 at 09:38 -0400, Ravi Varadhan wrote:
> There is nothing mysterious.  You need to increase the accuracy of
> quadrature by decreasing the error tolerance:
> 
> # I scaled your function to a proper Gaussian density
> shiftedGauss <- function(x0=500){
>  integrate(function(x) 1/sqrt(2*pi * 100^2) * exp(-(x-x0)^2/(2*100^2)), 0,
> Inf, rel.tol=1.e-07)$value }
> 
> shift <- seq(500, 800, by=10)
> plot(shift, sapply(shift, shiftedGauss))
> 
> 
> Hope this helps,
> Ravi.
> 
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of baptiste auguie
> Sent: Tuesday, September 21, 2010 8:38 AM
> To: r-help
> Subject: [R] puzzle with integrate over infinite range
> 
> Dear list,
> 
> I'm calculating the integral of a Gaussian function from 0 to
> infinity. I understand from ?integrate that it's usually better to
> specify Inf explicitly as a limit rather than an arbitrary large
> number, as in this case integrate() performs a trick to do the
> integration better.
> 
> However, I do not understand the following, if I shift the Gauss
> function by some amount the integral should not be affected,
> 
> shiftedGauss <- function(x0=500){
>  integrate(function(x) exp(-(x-x0)^2/100^2), 0, Inf)$value
> }
> 
> shift <- seq(500, 800, by=10)
> plot(shift, sapply(shift, shiftedGauss))
> 
> Suddenly, just after 700, the value of the integral drops to nearly 0
> when it should be constant all the way. Any clue as to what's going on
> here? I guess it's suddenly missing the important part of the range
> where the integrand is non-zero, but how could this be overcome?
> 
> Regards,
> 
> baptiste
> 
> 
> sessionInfo()
> R version 2.11.1 (2010-05-31)
> x86_64-apple-darwin9.8.0
> 
> locale:
> [1] en_GB.UTF-8/en_GB.UTF-8/C/C/en_GB.UTF-8/en_GB.UTF-8
> 
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
> 
> other attached packages:
> [1] inline_0.3.5        RcppArmadillo_0.2.6 Rcpp_0.8.6
> statmod_1.4.6
> 
> loaded via a namespace (and not attached):
> [1] tools_2.11.1
> 
> ______________________________________________
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> 
> ______________________________________________
> R-help at r-project.org mailing list
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Matthew S. Shotwell
Graduate Student 
Division of Biostatistics and Epidemiology
Medical University of South Carolina