[R] gnlr3 location parameter

[Arnout Standaert]

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)

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