Just be a little careful: you have omitted the ranges on your expressions, but is it not y > 0 for (1) and y > u for (2, corrected)? If so you will need to use bound-constrained optimization and worry about having a non-standard inference problem.
Prof Lindsey chooses not to submit his code to CRAN (nor even keep it that at a stable URL). As a result, few people here know about his packages and you would do better to ask him directly for support.
On Fri, 15 Apr 2005, Arnout Standaert wrote:
Hi list,
my previous question was obviously too basic to deserve an answer - apologies for that. I'm learning, things can only get better :-)
My current problem is with fitting a generalized gamma distribution with an additional "shift" parameter, that represents a shift of the distribution along the X axis.
The gnlr3 function (in Jim Lindsey's GNLM package) fits this distribution in this form:
f(y) = fy^(f-1)/((m/s)^(fs) Gamma(s)) y^(f(s-1)) exp(-(y s/m)^f) (1)
I would like to include a fourth parameter, say u, like this:
f(y) = fy^(f-1)/((m/s)^(fs) Gamma(s)) (y-u)^(f(s-1)) exp(-((y-u) s/m)^f) (2)
Is that right? Did you mean (y-u) near the front?
My best idea so far is to iteratively fit expression (1), each time shifting the data with an amount u. Plotting the maximum likelihood of the fit against u should give me an idea of where the optimum value for u is. Of course, this procedure will take quite some time, and will not be very straightforward since the generalized gamma shows convergence problems without good initial estimates...
Any suggestions for a better approach?
Thanks in advance, Arnout
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