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Quantile-quantile plot for data versus fitted gamma distribution

qgammavarname[ifexp] [inrange] [weight] [,alternativegridparam(# #)show(condition)generate(newvar)graph_options]where

graph_optionsare

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

fweights andaweights are allowed; see help weights.

Description

qgammaplots the quantiles ofvarnameagainst the quantiles of a two-parameter gamma distribution with probability density function for variablex>= 0, shape parametera> 0 and scale parameterb> 0 of [1 / (b^agamma(a))]x^(a- 1) exp(-x/b). See also thealternativeoption. By default, maximum likelihood estimation is carried out, using gammafit, which should be installed separately.

RemarksIn the majority of cases,

qgammawill be used to fit an gamma distribution on the fly and to assess that fit. In some cases, it may be of interest to compare data with a gamma 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

alternativespecifies use of an alternative parameterisation [(b^a/ gamma(a))]x^(a- 1) exp(-bx).

gridadds grid lines at the .05, .10, .25, .50, .75, .90, and .95 quantiles.

param()may be used to supply parameter values (namely, shape and scale 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 name of a new variable to hold values of fitted gamma quantiles.

graph_optionsarerlopts(cline_options),plot(plot)(Stata 8 only),addplot(plot)(Stata 9 up),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

. qgamma spacing

. qgamma spacing, param(20 3)

. qgamma spacing, gen(spacing_g)

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

ReferencesForbes, C., Evans, M., Hastings, N. and Peacock, B. 2011.

Statisticaldistributions.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 see