I don't have any experience with any of the families of
Johnson distributions, but I am not very surprised at
this. In my experience, difficulties of fitting
distributions often explode as the number of parameters
goes from 2 to 3 to 4. (There aren't many families much
talked about with 5 or more.) This may surprise mightily
anyone who is accustomed to fitting models with many
more parameters without difficulty. I surmise that the
nonlinearity of the problem is to blame, although that's
pinning a label on the issue rather than explaining it:
indeed Joseph's comments here are much more precise than
I can supply in this case.
Thanks for the references.
Nick
[email protected]
Joseph Coveney
> Nick Cox wrote about fitting distributions with -nl-. You
> can use this
> approach with -nl- (and -amoeba-) for fitting Johnson
> distributions, too,
> following Swain, Venkatraman and Wilson (1988). When you're
> in a region of
> the parameter space that is numerically nasty, such as is not
> infrequently
> the case with Johnson SB distributions, fitting by least
> squares like this
> often fails in my experience, even given starting values that
> are in the
> neighborhood of the minimum (maximum). Failure here means
> either failure to
> converge after a reasonable number of iterations, or wandering off and
> converging at a local minimum where the estimates are outside
> the parameter
> space. Sometimes in these cases, even when fed starting
> values right at the
> minimum, although it might not wander off, -nl- will give
> missing values for
> the standard errors of the coefficients, and associated t
> statistics and
> p-values for one or more of the Johnson parameter estimates. It seems
> that the curvature is nearly nil (or nearly infinite) at the
> minimum in
> these nasty cases (see Karian and Dudewicz). I've heard that
> least absolute
> deviation works better than least squares in these circumstances, but
> haven't
> looked into it. Putting constraints on parameter estimates
> in -nl- could
> also help in using it to fit Johnson distributions.
>
> Joseph Coveney
>
> J. J. Swain, S. Venkatraman and J. R. Wilson, Least-squares
> estimation of
> distribution functions in Johnson's translation system. J
> Statist Comput
> Simul 29:271--87, 1988.
>
> Z. A. Karian and E. J. Dudewicz, Computational issues in
> fitting statistical
> distributions to data.
> www.stat.auburn.edu/fsdd2006/papers/KarianDudewiczmain.pdf
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
