{smcl}
{* 19dec2006/17aug2011}{...}
{hline}
help for {hi:invgammafit}
{hline}
{title:Fitting a two-parameter inverse gamma distribution by maximum likelihood}
{p 8 17 2}
{cmd:invgammafit}
{it:varname}
[{it:weight}]
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}]
[{cmd:,}
{cmdab:alpha:var(}{it:varlist1}{cmd:)}
{cmdab:beta:var(}{it:varlist2}{cmd:)}
{cmdab:r:obust}
{cmdab:cl:uster(}{it:clustervar}{cmd:)}
{cmdab:l:evel(}{it:#}{cmd:)}
{it:maximize_options} ]
{p 4 4 2}{cmd:by} {it:...} {cmd::} may be used with
{cmd:invgammafit}; see help {help by}.
{p 4 4 2}{cmd:fweight}s and {cmd:aweight}s are allowed;
see help {help weights}.
{title:Description}
{p 4 4 2} {cmd:invgammafit} fits by maximum likelihood a two-parameter
inverse gamma distribution to a distribution of a variable
{it:varname}. The distribution has probability density function for
variable x > 0, shape parameter a > 0 and scale parameter
b > 0 of {bind:(b^a / Gamma(a)) x^(-a - 1) exp(-b / x)}.
{title:Options}
{p 4 8 2}{cmd:alphavar(}{it:varlist1}{cmd:)} and
{cmd:betavar(}{it:varlist2}{cmd:)} allow the user to specify each parameter as
a function of the covariates specified in the respective variable list. A
constant term is always included in each equation.
{p 4 8 2}{cmd:robust} specifies that the Huber/White/sandwich estimator of
variance is to be used in place of the traditional calculation; see
{hi:[U] 20.14 Obtaining robust variance estimates}. {cmd:robust} combined with
{cmd:cluster()} allows observations which are not independent within cluster
(although they must be independent between clusters).
{p 4 8 2}{cmd:cluster(}{it:clustervar}{cmd:)} specifies that the observations
are independent across groups (clusters) but not necessarily within groups.
{it:clustervar} specifies to which group each observation belongs; e.g.,
{cmd:cluster(personid)} in data with repeated observations on individuals. See
{hi:[U] 20.14 Obtaining robust variance estimates}. Specifying {cmd:cluster()}
implies {cmd:robust}.
{p 4 8 2}{cmd:level(}{it:#}{cmd:)} specifies the confidence level, in percent,
for the confidence intervals of the coefficients; see help {help level}.
{p 4 8 2}{cmd:nolog} suppresses the iteration log.
{p 4 8 2}{it:maximize_options} control the maximization process; see
help {help maximize}. If you are seeing many "(not concave)" messages in the
log, using the {cmd:difficult} option may help convergence.
{title:Remarks}
{p 4 4 2}This distribution is also described as the inverted gamma,
the reciprocal gamma, a Pearson Type V distribution and the Vinci
distribution.
{title:Saved results}
{p 4 4 2}In addition to the usual results saved after {cmd:ml}, {cmd:invgammafit}
also saves the following, if no covariates have been specified:
{p 4 4 2}{cmd:e(alpha)} and {cmd:e(beta)} are the estimated inverse
gamma parameters.
{p 4 4 2}The following results are saved regardless of whether covariates have
been specified:
{p 4 4 2}{cmd:e(b_alpha)} and {cmd:e(b_beta)} are row vectors containing the
parameter estimates from each equation.
{p 4 4 2}{cmd:e(length_b_alpha)} and {cmd:e(length_b_beta)} contain the lengths
of these vectors. If no covariates are specified in an equation, the
corresponding vector has length equal to 1 (the constant term); otherwise, the
length is one plus the number of covariates.
{title:Examples}
{p 4 8 2}{cmd:. invgammafit mpg}
{title:Authors}
{p 4 4 2}Nicholas J. Cox, Durham University{break}n.j.cox@durham.ac.uk
{p 4 4 2}Stephen P. Jenkins, London School of Economics{break}s.jenkins@lse.ac.uk
{title:Acknowledgments}
{p 4 4 2}Maarten Buis found a long-lurking bug.
{title:References}
{p 4 8 2}
Evans, M., Hastings, N. and Peacock, B. 2000. {it:Statistical distributions.}
New York: John Wiley.
{p 4 8 2}
Jeffreys, H. 1961. {it:Theory of probability.}
Oxford: Oxford University Press (see p.77).
{p 4 8 2}
Kleiber, C. and Kotz, S. 2003.
{it:Statistical size distributions in economics and actuarial sciences.}
Hoboken, NJ: John Wiley.
{title:Also see}
{p 4 13 2}
Online: help for
{help pinvgamma} (if installed),
{help qinvgamma} (if installed)