When the limits are infinite, it is not a good idea to use "large" but finite real numbers as approximate limits. It is best to use -Inf and/or +Inf. See the examples on the help page. Sometimes, setting a more stringent convergence criterion, i.e. decreasing rel.tol, helps, but it is best to use infinite limits.
I think this has to do with the transformation of the region of integration that is done in all the quadrature rules, so that the resulting region corresponds to appropriate regions for the corresponding orthogonal polynomials. For example, it is (-1, 1) for Gauss-Legendre quadrature. Ravi. ---------------------------------------------------------------------------- ------- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: rvarad...@jhmi.edu Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Allan Clark Sent: Monday, February 23, 2009 8:10 AM To: r-h...@stat.math.ethz.ch Subject: [R] r: intergrate behaviour hello R users strange behavior of the integrate function! i assume this occurs because of the way in which the quadriture is set up! (any comments.) f=function(x){exp(-exp(-x)-5*x)/gamma(5)} xx=seq(from=-20, to=20, length.out=1000) plot(xx,f(xx),type="l") integrate(f, lower=-Inf, upper= 1) integrate(f, lower=-Inf, upper= 10) integrate(f, lower=-10, upper= 11) integrate(f, lower=-Inf, upper= 11) integrate(f, lower=-Inf, upper= Inf) the results: > integrate(f, lower=-Inf, upper= 1) 0.9999586 with absolute error < 2.1e-06 > integrate(f, lower=-Inf, upper= 10) 1 with absolute error < 1.6e-06 > integrate(f, lower=-10, upper= 11) 1 with absolute error < 7.1e-06 > integrate(f, lower=-Inf, upper= 11) 1.375693e-06 with absolute error < 2.3e-06 > integrate(f, lower=-Inf, upper= Inf) 1 with absolute error < 3.1e-05 i dont get the same behaviour for J.K. Lindsey's int function. Allan Clark ======== Lecturer in Statistical Sciences Department University of Cape Town 7701 Rondebosch South Africa TEL (Office): +27-21-650-3228 FAX: +27-21-650-4773 http://web.uct.ac.za/depts/stats/aclark.htm [[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.