Selected Topics for Further Research - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 517

Fig. 12.46 Content of felsic metavolcanics in 64 square cells (Bathurst area, New Brunswick)
measuring 10 km on a side; Q - Q plot of cell values in Fig. 12.44 compared with line of best fit
(Source: Agterberg 2005 , Fig. 1)

frequency 1 - m ) and at x ¼ 1 (with frequency m ). For increasing cell size, for

example when a 4 km, the density function of X is U-shaped with densities

tending to infinity as x

¼

! 0 and as x ! 1. For larger cells, for example when

a 20 km, the distribution of X resembles a gamma distribution with density

tending to infinity as x

¼

0. Finally, for very large cells (not shown in
Fig. 12.45 ), the corresponding density function would become unimodal.
It is noted that this example was re-analyzed by Agterberg ( 1981 , Fig. 5) with
slightly different results as shown in the prob-prob plot of Fig. 12.46 . The broken
line in Fig. 12.46 is as in Fig. 12.44 obtained by estimating

!

from estimated
values of the mean and variance of the 64 cell values using Fig. 12.39 that gave the
estimates b

ʲ and ˁ

0.91, respectively. Figure 12.46 also shows a best-fitting
straight line obtained by linear regression of the quantile for frequency ( Y -axis) on
the quantile for composition ( X -axis). The intercept and slope of this best-fitting
line yielded estimates of 0.82 and 0.86 for

¼ 0.85 and r ¼

, respectively. The difference
between the two straight lines in Fig. 12.46 is probably due to the fact that on the Q -
Q plot more weight is given to points with larger relative frequencies. The best-
fitting straight line gives estimates that are probably slightly better than the straight
line derived from estimates of the mean and variance. This would be because the
smallest percentage values have greater relative errors than the larger percentage
values.

ʲ and ˁ