Hi Folks, This is not (well, not yet) an R question as such, though it is preparatory to embarking on an R-based study.
Scenario: X has a lognormal distribution. Jointly distributed with X is a "tag" Y: Y = 0 or 1, with Prob(Y=1|X) = exp(L)/(1+exp(L)), L = a + b*X I am interested in the distribution of X conditional on Y, which is proportional to f(x,Y) = dlnorm(x,mu,sigma)*exp(Y*L)/(1+exp(L)) (Y = 0 or 1, L = a + b*x) In particular, before gettiong down to the computational work, I am interested in studying its moments, and its "incomplete moments": Mj(X,Y) = Integral[x=0:X] x^j * f(x,Y) dx What I'd like to find out (and the chances are that some people on this list should know!) is what analytical forms may be available for such things. They are certainly known for the lognormal on its own, but the additional logistic factor has taken it beyond my immediate analytical capabilities. This has an obvious practical illustration: X may be a predictor for an event which, given X, has the logistic probability of occurring. The question relates therefore to the distrbution of X in cases where the event occurred, and in cases where the event did not occur. As such, I would expect that it has often turned up in the epidemiological world, and the resulting distribution may well have a name and well-known analytical properties. It just happens that I'm not acquainted with these! Any help will be much appreciated. With thanks, Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <[email protected]> Fax-to-email: +44 (0)870 094 0861 Date: 29-Dec-08 Time: 15:12:31 ------------------------------ XFMail ------------------------------ ______________________________________________ [email protected] 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.
