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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

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