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Probability plot for data versus fitted inverse Gaussian distribution

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

graph_optionsare

rlopts(cline_options)addplot(addplot)scatter_optionstwoway_options

fweights andaweights are allowed; see help weights.

Description

pinvgaussproduces a probability plot forvarnamecompared with a two-parameter inverse Gaussian distribution with probability density function variable x > 0, location parameter m > 0 and scale parameter l > 0 of (l / 2 pi x^3)^(1/2) exp((-l (x - m)^2 / 2 m^2 x)). By default, maximum likelihood estimation is carried out, using invgausscf, which should be installed separately.

RemarksIn the majority of cases,

pinvgausswill be used to fit an inverse Gaussian distribution on the fly and to assess that fit. In some cases, it may be of interest to compare data with a inverse Gaussian 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, location and scale parameters) directly for use in estimation of fitted quantiles. m and l 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 names of two new variables, the first to hold inverse Gaussian probabilities and the second to hold empirical probabilities.

graph_optionsarerlopts(cline_options),addplot(addplot),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.

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

. pinvgauss spacing

. pinvgauss spacing, param(20 3)

. pinvgauss spacing, gen(spacing_gam 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.

Also seeOnline: help for invgausscf, invgaussfit (if installed), qinvgauss (if installed), graph, diagplots