rvarad...@jhmi.edu
-Original Message-
From: Albyn Jones [mailto:jo...@reed.edu]
Sent: Thursday, December 02, 2010 6:41 PM
To: Ravi Varadhan
Cc: 'Hans W Borchers'; r-help@r-project.org
Subject: Re: [R] Integral of PDF
On Thu, Dec 02, 2010 at 06:23:45PM -0500, Ravi Varadhan wrote:
-project.org] On
Behalf Of Hans W Borchers
Sent: Friday, December 03, 2010 3:30 AM
To: r-help@r-project.org
Subject: Re: [R] Integral of PDF
That does not remedy the situation in any case, take the following function
fun <- function(x) dnorm(x, -500, 50) + dnorm(x, 500, 50)
that has a 'mo
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of Doran, Harold
Sent: 02 December 2010 21:22
To: r-help@r-project.org
Subject: [R] Integral of PDF
The integral of any probability density from -Inf to Inf should equal 1,
correct? I don't understand last result below
That does not remedy the situation in any case, take the following function
fun <- function(x) dnorm(x, -500, 50) + dnorm(x, 500, 50)
that has a 'mode' of 0 again. Interestingly, if I transform it by 1/x, to
integrate I again have to reduce the error tolerance to at least 1e-10:
On Thu, Dec 02, 2010 at 06:23:45PM -0500, Ravi Varadhan wrote:
> A simple solution is to locate the mode of the integrand, which should be
> quite easy to do, and then do a coordinate shift to that point and then
> integrate the mean-shifted integrand using `integrate'.
>
> Ravi.
Translation: t
Albyn's reply is in line with an hypothesis I was beginning to
formulate (without looking at the underlying FoRTRAN code),
prompted by the hint in '?integrate':
Details:
If one or both limits are infinite, the infinite range
is mapped onto a finite interval.
For a finite interval,
lto:r-help-boun...@r-project.org] On
Behalf Of Hans W Borchers
Sent: Thursday, December 02, 2010 5:16 PM
To: r-help@r-project.org
Subject: Re: [R] Integral of PDF
You can dive into the thread "puzzle with integrate over infinite range"
from September this year. The short answer app
gt; From: r-help-boun...@r-project.org
> [mailto:r-help-boun...@r-project.org] On Behalf Of Doran, Harold
> Sent: Thursday, December 02, 2010 1:22 PM
> To: r-help@r-project.org
> Subject: [R] Integral of PDF
>
> The integral of any probability density from -Inf to Inf
> should e
To really understaand it you will have to look at the fortran code
underlying integrate. I tracked it back through a couple of layers
(dqagi, dqagie, ... just use google, these are old netlib
subroutines) then decided I ought to get back to grading papers :-)
It looks like the integral is split
You can dive into the thread "puzzle with integrate over infinite range"
from September this year. The short answer appears to be: Increase the
error tolerance.
integrate(function(x) dnorm(x, 500,50), -Inf, Inf,
subdivisions=500, rel.tol=1e-11)
# 1 with absolute error < 1.1e
The integral of any probability density from -Inf to Inf should equal 1,
correct? I don't understand last result below.
> integrate(function(x) dnorm(x, 0,1), -Inf, Inf)
1 with absolute error < 9.4e-05
> integrate(function(x) dnorm(x, 100,10), -Inf, Inf)
1 with absolute error < 0.00012
> integr
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