vmcdf
"upper")Von Mises probability density function (PDF).
For each element of x, compute the cumulative distribution function (CDF) of the von Mises distribution with location parameter mu and concentration parameter k on the interval . The size of p is the common size of x, mu, and k. A scalar input functions as a constant matrix of the same same size as the other inputs.
p = vmcdf (x, mu, k, "upper") computes the
upper tail probability of the von Mises distribution with parameters mu
and k, at the values in x.
Note: the CDF of the von Mises distribution is not analytic. Hence, it is
calculated by integrating its probability density which is expressed as a
series of Bessel functions. Balancing between performance and accuracy, the
integration uses a step of 1e-5 on the interval ,
which results to an accuracy of about 10 significant digits.
Further information about the von Mises distribution can be found at https://en.wikipedia.org/wiki/Von_Mises_distribution
Source Code: vmcdf
## Plot various CDFs from the von Mises distribution
x1 = [-pi:0.1:pi];
p1 = vmcdf (x1, 0, 0.5);
p2 = vmcdf (x1, 0, 1);
p3 = vmcdf (x1, 0, 2);
p4 = vmcdf (x1, 0, 4);
plot (x1, p1, "-r", x1, p2, "-g", x1, p3, "-b", x1, p4, "-c")
grid on
xlim ([-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 CDF")
xlabel ("values in x")
ylabel ("probability")
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