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@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- View this message in context: http://r.789695.n4.nabble.com/Integral-of-PDF-tp3070243p3070315.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.