{smcl}
{* 17nov2003}{...}
{hline}
help for {hi:qgumbel} 
{hline}

{title:Quantile-quantile plot for data versus fitted Gumbel distribution}

{p 8 25 2}{cmd:qgumbel}{space 1}{it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{it:weight}] [{cmd:,} {cmdab:g:rid} 
{cmd:param(}{it:# #}{cmd:)} {cmd:show(}{it:condition}{cmd:)} 
{cmdab:gen:erate(}{it:newvar}{cmd:)} 
{it:graph_options} ]

{p 4 4 2}
where {it:graph_options} are

{p 8 8 2}
{cmd:rlopts(}{it:cline_options}{cmd:)}
{cmd:plot(}{it:plot}{cmd:)}
{it:scatter_options}
{it:twoway_options}

{p 4 4 2}{cmd:fweight}s and {cmd:aweight}s are allowed; see help {help weights}. 


{title:Description}

{p 4 4 2}
{cmd:qgumbel} plots the quantiles of {it:varname} against the quantiles of a
two-parameter Gumbel distribution with probability density function 
for variable {it:x}, scale parameter {it:a} > 0 and location parameter {it:m} 
of  (1 / {it:a}) exp[-({it:x} - {it:m}) / {it:a}] 
exp[-exp(-({it:x} - {it:m}) / {it:a})].  
By default, maximum likelihood estimation is carried out, using 
{help gumbelfit}, which should be installed separately. 


{title:Remarks} 

{p 4 4 2}In the majority of cases, {cmd:qgumbel} 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 {cmd:param()} option. In all cases
it is important not only to specify any {cmd:if} or {cmd:in} restrictions, but
also to specify relevant weights, which will (unless constant) affect the
configuration of the plot. 


{title:Options}

{p 4 8 2}{cmd:grid} adds grid lines at the .05, .10, .25, .50, .75, .90, and .95
quantiles. 

{p 4 8 2}{cmd:param()} may be used to supply parameter values (namely, scale 
and location parameters) directly for use in estimation of fitted quantiles. 
{it:a} and {it:m} should be provided as separate values in precisely that order.

{p 4 8 2}{cmd: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 {cmd:if} 
and {cmd:in} should not be used for this purpose. 

{p 4 8 2}{cmd:generate()} specifies the name of a new variable to hold values 
of fitted Gumbel quantiles. 

{p 4 8 2}{it:graph_options} are
{cmd:rlopts(}{it:cline_options}{cmd:)},
{cmd:plot(}{it:plot}{cmd:)},
{it:scatter_options}, and
{it:twoway_options}. 

{p 4 8 2}
{cmd:rlopts(}{it:cline_options}{cmd:)} affect the rendition of the reference
line; see help {help cline_options}.

{p 4 8 2}
{cmd:plot(}{it:plot}{cmd:)} provides a way to add other plots to the generated
graph; see help {help plot_option}.

{p 4 8 2}
{it:scatter_options} affect the rendition of the plotted points; see help
{help scatter}.

{p 4 8 2}
{it:twoway_options} are any of the options documented in help
{help twoway_options} excluding {cmd:by()}.  These include options for titling
the graph (see help {help title_options}) and options for saving the graph to
disk (see help {help saving_option}).


{title:Examples}

{p 4 8 2}{cmd:. qgumbel spacing}

{p 4 8 2}{cmd:. qgumbel spacing, param(20 3)}

{p 4 8 2}{cmd:. qgumbel spacing, gen(spacing_g)} 


{title:Author}

{p 4 4 2}Nicholas J. Cox, University of Durham, U.K.{break} 
n.j.cox@durham.ac.uk


{title:References}

{p 4 4 2}
Evans, M., Hastings, N. and Peacock, B. 2000. {it:Statistical distributions.}
New York: John Wiley.

{p 4 4 2} 
Johnson, N.L., Kotz, S. and Balakrishnan, N. 1995. 
{it:Continuous univariate distributions: Volume 2.} New York: John Wiley.


{title:Also see}

{p 4 13 2}
Online:  help for {help gumbelfit}, {help pgumbel} (if installed), {help graph}, {help diagplots}