Geoscience Reference
In-Depth Information
mu = 0; kappa = [0 1 2 3 4]';
We i rst dei ne an angle scale for a plot that runs from -180 to 180 degrees,
with intervals of one degree.
theta = -180:1:180;
All angles are converted from degrees to radians.
mu_radians = pi*mu/180;
theta_radians = pi*theta/180;
We then compute the von Mises distribution for these values. h e formula
uses the modii ed Bessel function of i rst kind and order zero that can be
calculated using the function
besseli
. We compute the probability density
function for the i ve values of
kappa
.
for i = 1:5
mises(i,:) = (1/(2*pi*besseli(0,kappa(i))))* ...
exp(kappa(i)*cos(theta_radians-mu_radians));
theta(i,:) = theta(1,:);
end
h e results are plotted by
for i = 1:5
plot(theta(i,:),mises(i,:))
axis([-180 180 0 max(mises(i,:))])
hold on
end
h e mean direction and concentration parameters of such theoretical
distributions can be easily modii ed for comparison with empirical
distributions.
10.5 Test for Randomness of Directional Data
h e i rst test for directional data compares the data set with a uniform
distribution. Directional data following a uniform distribution are purely
random, i.e., there is no preference for any direction. We use the ˇ
2
-test
(Section 3.8) to compare the empirical frequency distribution with the
theoretical uniform distribution. We i rst load our sample data.
clear
data_degrees_1 = load('directional_1.txt');
We then use the function
histogram
to count the number of observations
