Statistics: vminv

### Function Reference: `vminv`

statistics: x = vminv (p, mu, k)

Inverse of the von Mises cumulative distribution function (iCDF).

For each element of p, compute the quantile (the inverse of the CDF) of the von Mises distribution with location parameter mu and concentration parameter k on the interval [-pi,pi]. The size of x is the common size of p, mu, and k. A scalar input functions as a constant matrix of the same size as the other inputs.

Note: the quantile of the von Mises distribution is not analytic. Hence, it is approximated by a custom searching algorithm using its CDF until it converges up to a tolerance of `1e-5` or 100 iterations. As a result, balancing between performance and accuracy, the accuracy is about `5e-5` for `k = 1` and it drops to `5e-5` as k increases.

Further information about the von Mises distribution can be found at https://en.wikipedia.org/wiki/Von_Mises_distribution

See also: vmcdf, vmpdf, vmrnd

Source Code: vminv

### Example: 1

     ## Plot various iCDFs from the von Mises distribution
     p1 = [0,0.005,0.01:0.01:0.1,0.15,0.2:0.1:0.8,0.85,0.9:0.01:0.99,0.995,1];
     x1 = vminv (p1, 0, 0.5);
     x2 = vminv (p1, 0, 1);
     x3 = vminv (p1, 0, 2);
     x4 = vminv (p1, 0, 4);
     plot (p1, x1, "-r", p1, x2, "-g", p1, x3, "-b", p1, x4, "-c")
     grid on
     ylim ([-pi, pi])
     legend ({"μ = 0, k = 0.5", "μ = 0, k = 1", ...
              "μ = 0, k = 2", "μ = 0, k = 4"}, "location", "northwest")
     title ("Von Mises iCDF")
     xlabel ("probability")
     ylabel ("values in x")