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help for gumbelfit
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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