{smcl}
{* 19nov2003}{...}
{hline}
help for {hi:pbeta}
{hline}

{title:Probability plot for data versus fitted beta distribution}

{p 8 25 2}{cmd:pbeta}{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:newvar1 newvar2}{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:pbeta} produces a probability plot for {it:varname} compared with a
two-parameter beta distribution with probability density function
for variable 1 > {it:x} > 0, shape parameters {it:a} > 0
and {it:b} > 0 of  
[1 / {it:B}({it:a}, {it:b}) ] {it:x} ^({it:a} - 1) (1 -{it:x})^ ({it:b} - 1).  
Here {it:B}(,) is the beta function. 
By default, maximum likelihood estimation is carried out, using 
{help betafit}, which should be installed separately. 


{title:Remarks} 

{p 4 4 2}In the majority of cases, {cmd:pbeta} will be used to fit an
beta distribution on the fly and to assess that fit. In some cases, it
may be of interest to compare data with a beta 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} is equivalent to {cmd:yla(0(.25)1, grid) xla(0(.25)1, grid)}.

{p 4 8 2}{cmd:param()} may be used to supply parameter values (namely, shape 
parameters) directly for use in estimation of fitted quantiles. 
{it:a} and {it:b} 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 names of two new variables, 
the first to hold beta probabilities and the second to hold 
empirical probabilities. 

{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:. pbeta hail}

{p 4 8 2}{cmd:. pbeta hail, gen(hail_bet hail_emp)} 


{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 betafit}, {help qbeta} (if installed), {help graph}, {help diagplots}