Fitting a Gumbel distribution by maximum likelihood
gumbelfit varname [weight] [if exp] [in range] [, alphavar(varlist1) muvar(varlist2) robust cluster(clustervar) level(#) maximize_options ]
by ... : may be used with gumbelfit; see help by.
fweights and aweights are allowed; see help weights.
gumbelfit fits by maximum likelihood a two-parameter Gumbel distribution to a distribution of a variable varname. The distribution has probability density function for variable x, scale parameter alpha > 0 and location parameter mu of (1 / alpha) exp[-(x - mu) / alpha] exp[-exp(-(x - mu) / alpha)]. Note that x may be negative, zero or positive.
alphavar(varlist1) and muvar(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 the manual section in [U] on 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] on 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.
In addition to the usual results saved after ml, gumbelfit also saves the following, if no covariates have been specified:
e(alpha) and e(mu) are the estimated Gumbel parameters.
The following results are saved regardless of whether covariates have been specified:
e(b_alpha) and e(b_mu) are row vectors containing the parameter estimates from each equation.
e(length_b_alpha) and e(length_b_mu) 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.
. gumbelfit mpg
Nicholas J. Cox, Durham University email@example.com
Stephen P. Jenkins, London School of Economics firstname.lastname@example.org
Forbes, C., Evans, M., Hastings, N. and Peacock, B. 2011. Statistical distributions. Hoboken, NJ: John Wiley.
Johnson, N.L., Kotz, S. and Balakrishnan, N. 1995. Continuous univariate distributions: Volume 2. New York: John Wiley.
Online: help for pgumbel, qgumbel