You can use trace() to see what is happening > trace(dnorm, quote(print(round(x)))) > integrate(function(x) dnorm(x, 500,50), -Inf, Inf) Tracing dnorm(x, 500, 50) on entry [1] 1 233 0 38 0 14 0 7 0 4 0 2 0 2 1 Tracing dnorm(x, 500, 50) on entry [1] -1 -233 0 -38 0 -14 0 -7 0 -4 0 -2 0 -2 -1 Tracing dnorm(x, 500, 50) on entry [1] 3 467 1 78 1 29 1 14 1 9 2 6 2 4 2 Tracing dnorm(x, 500, 50) on entry [1] -3 -467 -1 -78 -1 -29 -1 -14 -1 -9 -2 -6 -2 -4 -2 Tracing dnorm(x, 500, 50) on entry [1] 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 Tracing dnorm(x, 500, 50) on entry [1] 0 -1 0 -1 0 -1 0 -1 0 -1 0 -1 0 0 0 Tracing dnorm(x, 500, 50) on entry [1] 7 935 3 156 3 58 3 30 4 18 4 12 5 9 6 Tracing dnorm(x, 500, 50) on entry [1] -7 -935 -3 -156 -3 -58 -3 -30 -4 -18 -4 -12 -5 -9 -6 Tracing dnorm(x, 500, 50) on entry [1] 2 3 1 3 1 3 1 3 1 2 1 2 1 2 1 Tracing dnorm(x, 500, 50) on entry [1] -2 -3 -1 -3 -1 -3 -1 -3 -1 -2 -1 -2 -1 -2 -1 8.410947e-11 with absolute error < 1.6e-10
You are asking integrate to find the relatively tiny portion of the the floating point real line (from c. -10^300 to 10^300) on which dnorm(x) is bigger than c. 10^-300. It found a few points where it was that big, but apparently not enough to home on the answer. You need to give it better hints abouts dnorm's support region. E.g., > integrate(function(x) dnorm(x, 500,50), -100, 900) Tracing dnorm(x, 500, 50) on entry [1] 400 -87 887 -33 833 60 740 183 617 326 474 -98 898 -65 865 10 790 119 681 [20] 253 547 Tracing dnorm(x, 500, 50) on entry [1] 150 -93 393 -66 366 -20 320 42 258 113 187 -99 399 -83 383 -45 345 9 291 [20] 76 224 Tracing dnorm(x, 500, 50) on entry [1] 650 407 893 434 866 480 820 542 758 613 687 401 899 417 883 455 845 509 791 [20] 576 724 Tracing dnorm(x, 500, 50) on entry [1] 525 403 647 417 633 440 610 471 579 506 544 401 649 409 641 427 623 455 595 [20] 488 562 Tracing dnorm(x, 500, 50) on entry [1] 775 653 897 667 883 690 860 721 829 756 794 651 899 659 891 677 873 705 845 [20] 738 812 1 with absolute error < 4.0e-07 Making the limits +-10^4 works ok also, but +-Inf is apparently asking for too much. Bill Dunlap Spotfire, TIBCO Software wdunlap tibco.com > -----Original Message----- > 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 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. > ______________________________________________ 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.