Actually, ignore the inverse_cdf function I have provided. It should generate a vlaue for kappa and it needs adjusting for values of thetahat other than zero.

Great submission. It would be nice to have cdf and inversion cdf for the vmpdf functions. Here's what I wrote for my needs
function p = circ_vmcdf(alpha, thetahat, kappa)
%integrates the pdf from an angle of -pi to an angle alpha
F = @(x)circ_vmpdf(x, thetahat, kappa);
p = quad(F,-pi(),alpha);
end

function theta = circ_vminv(p, thetahat, kappa)
%computes the inverse of the abovecirc_vmcdf.
fun =@(alpha)(circ_vmcdf(alpha, thetahat, kappa)-p);
theta = fzero(fun,[-pi pi]);
end