Geoscience Reference
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i.e. higher significant p-value is achieved where the z-value is far enough by the
bell peak of statistical normal distribution shape.
Z ¼
dN
ðÞ
d ra
ðÞ
SE
d ra
ðÞ
ð
4
Þ
The standard error of the mean random distance is calculated using Eq.
5
.
ð
4
p
Þ
A
4pN
2
0
:
26136
SQRT N
2
=
A
SE
d ra
ðÞ
SQRT
ð
5
Þ
More theoretical discussion about the NNI equations can be found in (Clark and
Evans
1954
). In this study, ''Average Nearest Neighbor'' function under Spatial
Statistics tools of ArcGIS software was used. The result file provided all the above
mentioned values such as; observed mean distance, expected mean distance,
nearest neighbor ratio, z-score, and p-value.
4.2 Evidential Belief Function (EBF) model
The Dempster-Shafer theory of evidence (belief) (Dempster
1968
; Shafer
1976
), is
a mathematical based model with a bivariate statistically methodology, used to
find the spatial integration based on the rule of combination. Generally, it is
applied successfully as knowledge based approach in mineral potential mapping
(Carranza
2009
).
Theory of belief is built up from direct mass function (Eq.
6
) to present 4 maps:
• Bel (degree of belief) as stated in Eqs.
7
and
8
,
• Dis (degree of disbelief) based on Eqs.
9
and
10
,
• Unc (degree of uncertainty) based on Eq.
11
, and;
• Pls (degree of plausibility) based on Eq.
12
. Which can handle the analysis even
with incomplete data coverage information (Carranza
2009
).
According to Dempster
1968
, the main parts of the theory is represented by Bel
(lower probability), and Pls (upper probability).
M : 2 ¼
f
[
;
Tp
;
Tp
; g
¼
f
Tp
;
Tp
g
ð
6
Þ
where:
Tp = class pixels affected by landslide
Tp
= class pixels not affected landslide
Equation
7
shows the ratio of Bel in each individual class of conditioning factor
and landslide ratio.
j T
ð
Eij ¼½N
ð
L
\
Eij
Þ=
N
ðÞ =
N Ei
ðÞ
NL
\
Eij
½
ð
Þ
Þ=ð
N
ðÞ
N
ð
L
Þ
¼ N
=
D
ð
7
Þ
