help for qinvgauss 

Quantile-quantile plot for data versus fitted inverse Gaussian distribution

qinvgauss varname [if exp] [in range] [weight] [, grid param(# #) show(condition) generate(newvar) graph_options ]

where graph_options are

rlopts(cline_options) addplot(plot) scatter_options twoway_options

fweights and aweights are allowed; see help weights.


qinvgauss plots the quantiles of varname against the quantiles of 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.


In the majority of cases, qinvgauss will 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 an inverse Gaussian distribution with known or hypothesised parameters, which may be specified using the param() option. In all cases it is important not only to specify any if or in restrictions, but also to specify relevant weights, which will (unless constant) affect the configuration of the plot.

Stata programmers will find embedded in the code various Mata functions for the inverse Gaussian that may be useful in other circumstances. The calculation of the quantile function is based in part on S code by Paul Bagshaw, found at http://www.statsci.org/s/invgauss.s (accessed 8 December 2006).


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

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 that if and in should not be used for this purpose.

generate() specifies the name of a new variable to hold values of fitted inverse Gaussian quantiles.

graph_options are rlopts(cline_options), addplot(plot) scatter_options, and twoway_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_options affect the rendition of the plotted points; see help scatter.

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


. qinvgauss spacing

. qinvgauss spacing, param(20 3)

. qinvgauss spacing, gen(spacing_g)


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


Evans, M., Hastings, N. and Peacock, B. 2000. Statistical distributions. New York: John Wiley.

Johnson, N.L., Kotz, S. and Balakrishnan, N. 1994. Continuous univariate distributions: Volume 1. New York: John Wiley.

Also see

Online: help for invgausscf, invgaussfit (if installed) pinvgauss (if installed), graph, diagplots