help for pgumbel

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.


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.


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.


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).


. pgumbel spacing

. pgumbel spacing, param(20 3)

. pgumbel spacing, gen(spacing_gum spacing_emp)


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


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