# [R] Integral of PDF

Hans W Borchers hwborchers at googlemail.com
Thu Dec 2 23:15:44 CET 2010

```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-12

Hans Werner

Doran, Harold wrote:
>
> 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
>
>> integrate(function(x) dnorm(x, 500,50), -Inf, Inf)
> 8.410947e-11 with absolute error < 1.6e-10
>
>> all.equal(integrate(function(x) dnorm(x, 500,50), -Inf, Inf)\$value, 0)
> [1] TRUE
>
>> sessionInfo()
> R version 2.10.1 (2009-12-14)
> i386-pc-mingw32
>
> locale:
> [1] LC_COLLATE=English_United States.1252  LC_CTYPE=English_United
> States.1252
> [3] LC_MONETARY=English_United States.1252 LC_NUMERIC=C
> [5] LC_TIME=English_United States.1252
>
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
>
> other attached packages:
> [1] statmod_1.4.6      mlmRev_0.99875-1   lme4_0.999375-35
> Matrix_0.999375-33 lattice_0.17-26
>
> loaded via a namespace (and not attached):
> [1] grid_2.10.1   nlme_3.1-96   stats4_2.10.1 tools_2.10.1
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help