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

{title:Probability plot for von Mises distribution fitted to circular data}

{p 8 17 2}
{cmd:circpvm}
{it:varname} 
[{cmd:if} {it:exp}] 
[{cmd:in} {it:range}]
[{cmd:, a(}{it:#}{cmd:)}
{cmdab:g:rid}
{cmd:plot(}{it:plot}{cmd:)}
{it:scatter_options}] 


{title:Description}

{p 4 4 2}
{cmd:circpvm} gives a probability (P-P) 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. 

{p 4 4 2}For discussion, see Jammalamadaka and SenGupta (2001, pp.218-219);  
but note that some of their discussion of P-P plots applies to 
quantile-quantile plots (Q-Q plots), not P-P plots.  


{title:Options}

{p 4 8 2}{cmd:a()} specifies {it:a} in the formula for plotting position.  The
plotting positions are ({it:i} - {it:a}) / ({it:n} - 2{it:a} + 1) for values 
ranked smallest to largest and assigned unique ranks {it:i} = 1, ..., {it:n}. 
The default is {it:a} = 0.5, giving ({it:i} - 0.5) / {it:n}.  
Other choices include {it:a} = 0, giving {it:i} /
({it:n} + 1), and {it:a} = 1/3, giving ({it:i} - 1/3) / ({it:n} + 1/3).

{p 4 8 2}
{cmd:grid} is equivalent to {cmd:yla(0(.25)1, grid) xla(0(.25)1, grid)}. 

{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 options of {help scatter}. 


{title:Examples}

{p 4 4 2}{cmd:. circpvm wallasp} 


{title:References}

{p 4 8 2}
Jammalamadaka, S.R. and SenGupta, A. 2001. 
{it:Topics in circular statistics.} Singapore: World Scientific.


{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 circqvm}