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help for gammafit
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Fitting a two-parameter gamma distribution by maximum likelihood

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

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

    fweights and aweights are allowed; see help weights.


Description

    gammafit fits by maximum likelihood a two-parameter 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 [1 / (b^a gamma(a))] x^(a - 1) exp(-x / b).  See also
    the alternative option.


Options

    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.

    alternative specifies use of an alternative parameterisation [(b^a /
        gamma(a))] x^(a - 1) exp(-bx).

    robust specifies that the Huber/White/sandwich estimator of variance is
        to be used in place of the traditional calculation; see [U] 23.14
        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] 23.14 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.


Saved results

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

    e(alpha) and e(beta) are the estimated 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.

        
Examples

    . gammafit 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. 1994.  Continuous univariate
    distributions: Volume 1. New York: John Wiley.

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


Also see

    Online: help for pgamma (if installed), qgamma (if installed)