Hi, Simply re-write your integrand as follows:
integrand <- function(X) {0.5 * cos(theta) * 2 / (exp(-pi*X/2 - X*theta) + exp(pi*X/2 - X*theta)) } Now the problem goes away. > theta <- -1 > integrate(integrand, -Inf, 1) 0.9842315 with absolute error < 1.2e-05 This would work for all theta such that abs(theta) < -pi/2. 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: [EMAIL PROTECTED] Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ---------------------------------------------------------------------------- -------- -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of xia wang Sent: Tuesday, August 26, 2008 1:01 AM To: r-help@r-project.org Subject: [R] Problem with Integrate for NEF-HS distribution I need to calcuate the cumulative probability for the Natural Exponential Family - Hyperbolic secant distribution with a parameter theta between -pi/2 and pi/2. The integration should be between 0 and 1 as it is a probability. The function "integrate" works fine when the absolute value of theta is not too large. That is, the NEF-HS distribution is not too skewed. However, once the theta gets large in absolute value, such as -1 as shown in the example below, "integrate" keeps give me error message for "non-finite function" when I put the lower bound as -Inf. I suspect that it is caused by the very heavy tail of the distribution. Is there any way that I can get around of this and let "integrate" work for the skewed distribution? Or is there any other function for integrating in R-package? Thanks a lot for your advice in advance! > theta<--1 > sech<-function(X) 2/(exp(-X)+exp(X)) > integrand <- function(X) {0.5*cos(theta)*exp(X*theta)*sech(pi*X/2)} > integrate(integrand, -3,1) 0.8134389 with absolute error < 7e-09 > integrate(integrand, -10,1) 0.9810894 with absolute error < 5.9e-06 > integrate(integrand, -15,1) 0.9840505 with absolute error < 7e-09 > integrate(integrand, -50,1) 0.9842315 with absolute error < 4.4e-05 > integrate(integrand, -100,1) 0.9842315 with absolute error < 3.2e-05 > integrate(integrand, -Inf,1) Error in integrate(integrand, -Inf, 1) : non-finite function value Xia _________________________________________________________________ Be the filmmaker you always wanted to be-learn how to burn a DVD with WindowsR. ______________________________________________ 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.