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Probability plot for data versus fitted Weibull distribution

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

graph_optionsare

rlopts(cline_options)plot(plot)addplot(plot)scatter_optionstwoway_options

fweights andaweights are allowed; see help weights.

Description

pweibullproduces a probability plot forvarnamecompared with a two-parameter Weibull distribution with probability density function for variablex>= 0, scale parameterb> 0 and shape parameterc> 0 of (c/b) (x/b)^(c- 1) exp(-(x/b)^c). By default, maximum likelihood estimation is carried out by weibullfit.

RemarksIn the majority of cases,

pweibullwill be used to fit an Weibull distribution on the fly and to assess that fit. In some cases, it may be of interest to compare data with a Weibull 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, scale and shape parameters) directly for use in estimation of fitted quantiles.bandcshould 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 Weibull probabilities and the second to hold empirical probabilities.

graph_optionsarerlopts(cline_options),plot(plot),addplot(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 (Stata 8 only).

addplot(plot)provides a way to add other plots to the generated graph; see help addplot_option (Stata 9 up).

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

. pweibull spacing

. pweibull spacing, param(20 3)

. pweibull spacing, gen(spacing_wei spacing_emp)

AuthorNicholas J. Cox, Durham University, 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. 1994.

Continuous univariatedistributions: Volume 1.New York: John Wiley.Kleiber, C. and Kotz, S. 2003.

Statistical size distributions ineconomics and actuarial sciences.Hoboken, NJ: John Wiley.

Also seeOnline: help for qweibull (if installed), weibullfit, graph