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st: Fit GB2, Singh-Maddala, Dagum, Lognormal distributions by ML


From   "Stephen P. Jenkins" <stephenj@essex.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   st: Fit GB2, Singh-Maddala, Dagum, Lognormal distributions by ML
Date   Sun, 18 Mar 2007 23:06:05 -0000 (GMT)

Some additional programs for fitting distributions by maximum likelihood are now
available to download from SSC (with thanks, as ever, to Kit Baum).

The distributions that can be fitted are:

Generalized Beta of the Second Kind (4 parameter): module -gb2fit-
Dagum (3 parameter): module -dagumfit-
Singh-Maddala (3 parameter): module -smfit-
Lognormal (2 parameter): module -lognfit-

All programs have a similar look and feel, and have associated prediction programs.
In each case, the parameters can be modelled as linear functions of covariates.(NB
-smfit- and -dagumfit- are updates to programs first placed on SSC in 1997.)

I have not had time to prepare a full write-up of the programs since they were
originally written in 2004, as originally intended, and so am releasing them now '
as is'. Potential users may find the following useful as an introductory guide:

    Jenkins, S.P. (2004). Fitting functional forms to distributions, using -ml-.
Presentation at Second German Stata Users Group Meeting, Berlin. 
http://www.stata.com/meeting/2german/Jenkins.pdf

Please note that Nick Cox has written programs for assessing goodness of fit
graphically, for each of the program modules cited above, and he will be placing
the modules on SSC shortly.

Thanks to Nick Cox for writing these programs, and for chivvying me along on my 
work, as well as providing useful comments and suggestions. Brian Bucks also
provided useful comments and suggestions. Time permitting, the programs will be
developed further.

-------------------------------------------------
TITLE
      'GB2FIT': module to fit Generalized Beta of the Second Kind distribution by
maximum likelih
> ood

DESCRIPTION/AUTHOR(S)

        gb2fit fits by ML the 4 parameter Generalized Beta distribution
      of the second kind (GB2) to sample observations    on a random
      variable.  gb2pred calculates statistics summarizing a GB2
      distribution which has been fitted using gb2fit. Unit record
      data are assumed (rather than grouped data). The    Singh-Maddala
      (1976) distribution is the special case when parameter p = 1, and
      the Dagum (1977, 1980)    distribution is the special case when
      parameter q = 1. The GB2 distribution has been shown to provide a
      good fit to data on  income but, of course, it might also be
      suitable for describing any skewed variable, not only income.

      KW: Generalized Beta of the Second Kind
      KW: GB2
      KW: inequality
      KW: maximum likelihood

      Requires: Stata version 8.2

      Distribution-Date: 20070316

      Author: Stephen P. Jenkins, University of Essex
      Support: email stephenj@essex.ac.uk


INSTALLATION FILES                               (type net install gb2fit)
      gb2fit.ado
      gb2fit_ll.ado
      gb2fit.hlp
      gb2pred.ado
      gb2pred.hlp
-------------------------------------------------------------------------------------------------
(type -ssc install gb2fit- to install)



-- 
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/
Downloadable papers and software: http://ideas.repec.org/e/pje7.html

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