Dear all: First, apologies for cross-posting multiplicities and for a query that is more analytically related than S-language related. The bottom-line wish is: Could you please provide and advice, references, etc on S software approaches for fitting a distribution with density: p*g(x) + (1-p)*f(x) where g(x) is the familiar lognormal 2-parameter density and f(x) is Pareto as defined below? Here is the lengthier story: I am collaborating with a scientific colleague who has constructed a database of binding assay data, namely EC/IC50's across a wide variety of chemical entities and experimental conditions. Among other things, he has an interest in characterizing tails of the distribution. We have been studying various fields in the literature to get a sense of what density forms we should focus on. In addition to lognormal, weibull, & gamma, we found several references to the Pareto distribution. It is of course easy enough to fit all of these with existing S language functions (and reference to MASS and S Programming), and even when considering lognormal mixtures as we are. However, I have been attempting to use the Pareto density form f(x) = ( a * k^a ) / ( x^{a + 1} ) ; k > 0, a > 0, x >= k as part of a mixture with a lognormal. Reparametrizing the density to f(x) = ( a * k^a ) / ( (x + k)^{a + 1} ) ; k > 0, a > 0, x > 0 seems to help but the optimization routines remain balky and / or give convergences that do not make sense to me. (I understand that starting values, scales, etc. are very important.) I suspect that the support aspect of the Pareto ( i.e. f(x) > 0 only for x >= k ) imposes an indentifiability problem with the mixing proportion parameter. Again, any advice is welcome. Thanks in advance, Bill ---------------------------------------- Bill Pikounis, Ph.D. Biometrics Research Department Merck Research Laboratories PO Box 2000, MailDrop RY70-38 126 E. Lincoln Avenue Rahway, New Jersey 07065-0900 USA v_bill_pikounis at merck.com Phone: 732 594 3913 Fax: 732 594 1565 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._