{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}