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Fig. 3.11 Three-parameter lognormal model for gold values in Merriespruit Mine, Witwatersrand
goldeld, South Africa (After Sichel
1961
, Fig. 2; original data from Krige
1960
). Because of the
additional peak at zero, the corresponding cumulative frequency distribution curve is normal for
gold values that are positive only. Note that this situation differs from that in Fig.
3.10
, although
the transformation is of the same type (Source: Agterberg
1974
, Fig. 32)
South Africa after 1971. The original inch-dwt value represented the amount of
gold present in a column of ore with a base of one square inch and perpendicular to
the reef. The best-tting normal curve shown in Fig.
3.11
was originally derived by
Sichel (
1961
). It was tted to all values except those at zero which form a sharp,
secondary peak.
3.2.4 Graphical Method for Reconstructing the Generating
Process
The starting point of the preceding discussion of the generating process also can be
written as
dX
i
¼
X
i1
in innites-
imal form. Several systems of curve-tting are in existence for relating an observed
frequency distribution to a normal form. An example of this is Johnson's (
1949
)
system which makes use of
dX
i
¼
g
(
X
i
)·
ʵ
i
where
dX
i
represents the difference
X
i
ʵ
i
. An excellent review of curve-tting
systems was given by Kendall and Stuart (
1949
). The so-called Johnson S
B
-system
results in lognormal distribution of the variable
X
/(1 +
X
). Jizba (
1959
) used this
approach for modeling geochemical systems. It may be possible to obtain informa-
tion on the nature of the function
g
(
X
i
) by graphical analysis using the normal
Q
-
Q
plot. This method is illustrated in Fig.
3.12
for a lognormal situation.
In Fig.
3.12a
, a lognormal curve was plotted on normal probability paper. An
auxiliary variable
z
is plotted along the horizontal axis. It has the same arithmetic
scale as
x
that is plotted in the vertical direction. The variable
x
is a function of
z
or
g
(
X
i
)·
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