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help for pgumbel
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Probability plot for data versus fitted Gumbel distribution

        pgumbel varname [if exp] [in range] [weight] [, grid param(# #)
                         show(condition) generate(newvar1 newvar2)
                         graph_options ]

    where graph_options are

        rlopts(cline_options) plot(plot) scatter_options twoway_options

    fweights and aweights are allowed; see help weights.


Description

    pgumbel produces a probability plot for varname compared with a
    two-parameter Gumbel distribution with probability density function for
    variable x, scale parameter a > 0 and location parameter m of (1 / a)
    exp[-(x - m) / a] exp[-exp(-(x - m) / a)].  By default, maximum
    likelihood estimation is carried out, using gumbelfit, which should be
    installed separately.


Remarks 

    In the majority of cases, pgumbel will be used to fit an Gumbel
    distribution on the fly and to assess that fit. In some cases, it may be
    of interest to compare data with a Gumbel distribution with known or
    hypothesised parameters, which may be specified using the param() option.
    In all cases it is important not only to specify any if or in
    restrictions, but also to specify relevant weights, which will (unless
    constant) affect the configuration of the plot.


Options

    grid is equivalent to yla(0(.25)1, grid) xla(0(.25)1, grid).

    param() may be used to supply parameter values (namely, scale and
        location parameters) directly for use in estimation of fitted
        quantiles.  a and m should be provided as separate values in
        precisely that order.

    show() may be used to specify that you wish to restrict the graph
        according to some condition, say looking at one tail of the
        distribution only. Note that if and in should not be used for this
        purpose.

    generate() specifies the names of two new variables, the first to hold
        Gumbel probabilities and the second to hold empirical probabilities.

    graph_options are rlopts(cline_options), plot(plot), scatter_options, and
        twoway_options.

    rlopts(cline_options) affect the rendition of the reference line; see
        help cline_options.

    plot(plot) provides a way to add other plots to the generated graph; see
        help plot_option.

    scatter_options affect the rendition of the plotted points; see help 
        scatter.

    twoway_options are any of the options documented in help twoway_options
        excluding by().  These include options for titling the graph (see
        help title_options) and options for saving the graph to disk (see
        help saving_option).


Examples

    . pgumbel spacing

    . pgumbel spacing, param(20 3)

    . pgumbel spacing, gen(spacing_gum spacing_emp)


Author

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


References

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

    Johnson, N.L., Kotz, S. and Balakrishnan, N. 1995.  Continuous univariate
    distributions: Volume 2. New York: John Wiley.


Also see