{smcl}
{* 3may2004}{...}
{hline}
help for {hi:circqvm}
{hline}

{title:Quantile-quantile plot for von Mises distribution fitted to circular data}

{p 8 17 2}
{cmd:circqvm} 
{it:varname} 
[{cmd:if} {it:exp}] 
[{cmd:in} {it:range}]
[{cmd:, show(}{it:numlist}{cmd:)}
{cmd:plot(}{it:plot}{cmd:)}
{it:scatter_options}] 


{title:Description}

{p 4 4 2}
{cmd:circqvm} gives a quantile-quantile plot for the fit of a 
von Mises (a.k.a. circular normal) distribution to a circular variable 
on a scale between 0 and 360 degrees. {help circvm} is used 
to fit the distribution, estimating the two parameters vector mean mu 
and concentration parameter kappa. Both observed and expected quantiles 
are rotated so that each set is centred on the observed vector mean. 
Each is nevertheless labelled in terms of {it:varname}. 

{p 4 4 2}This plot was suggested by Fisher (1993). However, he  
uses a sine((angle - centre) / 2) scale, which has the merit of 
pulling in the tails and stretching the region near the centre
of the distribution, but the disadvantage, as with any 
transformation, of being one step further away from the data. 


{title:Options}

{p 4 8 2} 
{cmd:show()} specifies a numlist of axis labels to be shown, overriding the 
default.

{p 4 8 2}
{cmd:plot(}{it:plot}{cmd:)} provides a way to add other plots to the generated
graph; see help {help plot_option}.

{p 4 8 2} 
{it:scatter_options} are any options allowed with {help scatter}.  


{title:Examples}

{p 4 4 2}{cmd:. circqvm wallasp}{p_end} 
{p 4 4 2}{cmd:. circqvm wallasp, show(0(45)315)}


{title:References}

{p 4 8 2}
Fisher, N.I. 1993. {it:Statistical analysis of circular data.}
Cambridge: Cambridge University Press.


{title:Author}

{p 4 4 2}Nicholas J. Cox, University of Durham, U.K.{break} 
         n.j.cox@durham.ac.uk


{title:Also see}

{p 4 13 2}
On-line: help for {help circvm}, {help circpvm}