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
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