help for gumbelfit

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.

Description

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.

Options

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.

Saved results

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.

Examples

. gumbelfit mpg

Authors

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

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

References

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.

Also see

Online: help for pgumbel, qgumbel