Notice: On April 23, 2014, Statalist moved from an email list to a forum, based at statalist.org.

# Re: st: q-q plots, theoretical distribution with values higher than the sample's cutoff point

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: q-q plots, theoretical distribution with values higher than the sample's cutoff point Date Fri, 20 Jul 2012 12:44:51 -0400

```Nick,

You're correct that, in general, the g-and-h distributions do not have
closed-form densities or cumulative distribution functions.  The
quantile function doesn't exist in closed form either, but only
because the quantile function of the normal distribution is not
closed-form.

For reasons of resistance and robustness, I usually prefer to work
with quantiles.  Fitting by maximum likelihood opens you up to
problems when the distribution has heavy tails and the data may
contain outliers.  Nowadays, fitting a g-and-h distribution by maximum
likelihood is not a major problem, but it is not just a few lines of
code!  I don't know how much has been done on fitting models that
involve predictors.  In any event, the g-and-h distributions are a
valuable part of my toolkit, but not a panacea.

I have no basic problem with maximum likelihood.  I've made heavy use
of it, in Stata and elsewhere.  But good data analysis is iterative:
one should look at data and residuals at various stages.

David Hoaglin

On Fri, Jul 20, 2012 at 10:29 AM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> Fair question for me at the end. I mean that g- and h- distributions are despite their flexibility rather awkward or elusive customers. It may be just psychology or convenience, but I like distributions with relatively simple closed-form definitions of density, distribution and quantile functions so that I can write a few lines of code to fit them by maximum likelihood, etc. Correct me if I am wrong, but g- and h- don't score well under that heading. As David implies, the practical problem is usually fitting a distribution given predictors, and fitting easily into the ML framework is to me highly desirable.

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```