help for invgammafit

Fitting a two-parameter inverse gamma distribution by maximum likelihood

invgammafit varname [weight] [if exp] [in range] [, alphavar(varlist1) betavar(varlist2) robust cluster(clustervar) level(#) maximize_options ]

by ... : may be used with invgammafit; see help by.

fweights and aweights are allowed; see help weights.


invgammafit fits by maximum likelihood a two-parameter inverse gamma distribution to a distribution of a variable varname. The distribution has probability density function for variable x > 0, shape parameter a > 0 and scale parameter b > 0 of (b^a / Gamma(a)) x^(-a - 1) exp(-b / x).


alphavar(varlist1) and betavar(varlist2) 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.

robust specifies that the Huber/White/sandwich estimator of variance is to be used in place of the traditional calculation; see [U] 20.14 Obtaining robust variance estimates. robust combined with cluster() allows observations which are not independent within cluster (although they must be independent between clusters).

cluster(clustervar) specifies that the observations are independent across groups (clusters) but not necessarily within groups. clustervar specifies to which group each observation belongs; e.g., cluster(personid) in data with repeated observations on individuals. See [U] 20.14 Obtaining robust variance estimates. Specifying cluster() implies robust.

level(#) specifies the confidence level, in percent, for the confidence intervals of the coefficients; see help level.

nolog suppresses the iteration log.

maximize_options control the maximization process; see help maximize. If you are seeing many "(not concave)" messages in the log, using the difficult option may help convergence.


This distribution is also described as the inverted gamma, the reciprocal gamma, a Pearson Type V distribution and the Vinci distribution.

Saved results

In addition to the usual results saved after ml, invgammafit also saves the following, if no covariates have been specified:

e(alpha) and e(beta) are the estimated inverse gamma parameters.

The following results are saved regardless of whether covariates have been specified:

e(b_alpha) and e(b_beta) are row vectors containing the parameter estimates from each equation.

e(length_b_alpha) and 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.


. invgammafit mpg


Nicholas J. Cox, Durham University n.j.cox@durham.ac.uk

Stephen P. Jenkins, London School of Economics s.jenkins@lse.ac.uk


Maarten Buis found a long-lurking bug.


Evans, M., Hastings, N. and Peacock, B. 2000. Statistical distributions. New York: John Wiley.

Jeffreys, H. 1961. Theory of probability. Oxford: Oxford University Press (see p.77).

Kleiber, C. and Kotz, S. 2003. Statistical size distributions in economics and actuarial sciences. Hoboken, NJ: John Wiley.

Also see

Online: help for pinvgamma (if installed), qinvgamma (if installed)