Dear All, thanks in advance for your attention. I'm struggling with this for a few weeks now, and figured it's time to get some help. I want to
integrate(f(x), lower=-Inf, upper=Inf) with f(x) = ((gamma(K+1)/(gamma(r+1)*gamma(K-r+1)))*(q(x)^r)*(((1-q(x))^(K-r))*phi(x), where phi(x) is the standard normal pdf, and q(x) the logistic CDF (with inverse scale parameter, so a little reparameterized). In short: it's a compound binomial probability. It can be shown that this integral can be expressed as a sum of moments of the System-Bounded Johnson distribution, for which it is proven that no analytical expressions exist. Moreover, it can be written as an infinite Taylor series in terms of moments of the lognormal distribution, but this series doesn't converge in general. Numerical integration is the only way to go. The problem is that integrate() is not accurate enough. I cannot compensate using rel.tol, since there is always a trade-off between "integral is probably divergent" and "roundoff error detected". I've read about the Rmpfr package, but this doesn't seem like an elegant way to proceed. I'm looking forward to your input. Thanks in advance! Cheers, Thomas -- View this message in context: http://r.789695.n4.nabble.com/Integrate-compound-distribution-tp4637735.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.
