Geoscience Reference
In-Depth Information
mean_radians_1 =
0.7546
mean_degrees_1 =
43.2357
h is result suggests that the resultant vector R is around 0.75 radians or 43°.
However, since both
x
and
y
are negative, the true value of
mean_degrees
is
located in the third quadrant and we therefore add 180°
mean_degrees_1 = mean_degrees_1 + 180
mean_degrees_1 =
223.2357
which results in a mean direction of around 223°. h e length of this vector is
the absolute value of the vector, which is
R_1 = sqrt(x_1^2 + y_1^2)
R_1 =
35.6055
h e resultant length depends on the dispersion of the directional data.
Normalizing the resultant length to the sample size yields the mean resultant
length
Rm
of
Rm_1 = R_1 / (length(data_radians_1))
Rm_1 =
0.8901
A high
Rm
value suggests less variance. We then compute the circular variance
sigma
, which is
sigma_1 = 1 - Rm_1
sigma_1 =
0.1099
10.4 Theoretical Distributions
As in Chapter 3, the next step in a statistical analysis is to i nd a suitable
theoretical distribution that we i t to the empirical distribution visualized
and described in the previous section. h e classic theoretical distribution
to describe directional data is the
von Mises distribution
, named at er
the Austrian mathematician Richard Edler von Mises (1883-1953). h e
probability density function of a von Mises distribution is
