Geoscience Reference
In-Depth Information
where ʼ is the mean direction and ʺ is the concentration parameter (Mardia
and Jupp 2000) (Fig. 10.5).
I
0
(ʺ) is the modii ed Bessel function of i rst
kind and order zero. h e Bessel functions are solutions of a second-order
dif erential equation (Bessel's dif erential equation) and are important in
many problems of wave propagation in a cylindrical waveguide, and of
heat conduction in a cylindrical object. h e von Mises distribution is also
known as the circular normal distribution since it has similar characteristics
to a normal distribution (Section 3.4). h e von Mises distribution is used
when the mean direction is the most frequent direction. h e probability of
deviations is equal on either side of the mean direction and decreases with
increasing distance from the mean direction.
As an example let us assume a mean direction of
mu=0
and i ve dif erent
values for the concentration parameter
kappa
.
clear
Fig. 10.5
Probability density function
f
(
x
) of a von Mises distribution with ʼ=0 and i ve
dif erent values for ʺ.
