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Probability plot for data versus fitted beta distribution

pbetavarname[ifexp] [inrange] [weight] [,gridparam(# #)show(condition)generate(newvar1 newvar2)graph_options]where

graph_optionsare

rlopts(cline_options)plot(plot)scatter_optionstwoway_options

fweights andaweights are allowed; see help weights.

Description

pbetaproduces a probability plot forvarnamecompared with a two-parameter beta distribution with probability density function for variable 1 >x> 0, shape parametersa> 0 andb> 0 of [1 /B(a,b) ]x^(a- 1) (1 -x)^ (b- 1). HereB(,) is the beta function. By default, maximum likelihood estimation is carried out, using betafit, which should be installed separately.

RemarksIn the majority of cases,

pbetawill 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 theparam()option. In all cases it is important not only to specify anyiforinrestrictions, but also to specify relevant weights, which will (unless constant) affect the configuration of the plot.

Options

gridis equivalent toyla(0(.25)1, grid) xla(0(.25)1, grid).

param()may be used to supply parameter values (namely, shape parameters) directly for use in estimation of fitted quantiles.aandbshould 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 thatifandinshould not be used for this purpose.

generate()specifies the names of two new variables, the first to hold beta probabilities and the second to hold empirical probabilities.

graph_optionsarerlopts(cline_options),plot(plot),scatter_options, andtwoway_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_optionsaffect the rendition of the plotted points; see help scatter.

twoway_optionsare any of the options documented in help twoway_options excludingby(). These include options for titling the graph (see help title_options) and options for saving the graph to disk (see help saving_option).

Examples

. pbeta hail

. pbeta hail, gen(hail_bet hail_emp)

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

ReferencesEvans, M., Hastings, N. and Peacock, B. 2000.

Statistical distributions.New York: John Wiley.Johnson, N.L., Kotz, S. and Balakrishnan, N. 1995.

Continuous univariatedistributions: Volume 2.New York: John Wiley.

Also see