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Quantile-quantile plot for data versus fitted inverse gamma distribution

qinvgammavarname[ifexp] [inrange] [weight] [,gridparam(# #)show(condition)generate(newvar)graph_options]where

graph_optionsare

rlopts(cline_options)plot(plot)(Stata 8 only)addplot(plot)(Stata 9 only)scatter_optionstwoway_options

fweights andaweights are allowed; see help weights.

Description

qinvgammaplots the quantiles ofvarnameagainst the quantiles of a two-parameter inverse gamma distribution with probability density function for variable x > 0, shape parameter a > 0 and scale parameter b > 0 of (b^a / Gamma(a)) x^(-a - 1) exp(-b / x). By default, maximum likelihood estimation is carried out, using invgammafit, which should be installed separately.

RemarksIn the majority of cases,

qinvgammawill be used to fit an inverse gamma distribution on the fly and to assess that fit. In some cases, it may be of interest to compare data with an inverse 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.Stata programmers will find appended to the code various Mata functions for the inverse gamma that may be useful in other circumstances.

Options

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. a and b should 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 inverse gamma quantiles.

graph_optionsarerlopts(cline_options),addplot(plot)(Stata 9 only),plot(plot)(Stata 8 only),scatter_options, andtwoway_options.

rlopts(cline_options)affect the rendition of the reference line; see help cline_options.

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

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

. qinvgamma spacing

. qinvgamma spacing, param(20 3)

. qinvgamma spacing, gen(spacing_g)

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.Kleiber, C. and Kotz, S. 2003.

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

Also seeOnline: help for invgammafit, pinvgamma (if installed), graph, diagplots