Maximum Likelihood, Lognormality and Compound Distributions - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 92

Fig. 3.8 (a). Plot on logarithmic probability paper of histogram for 116 copper determinations
from gabbros in the Muskox intrusion. (b). Separate plots for different types of gabbro show that
curve in a actually represent a mixture of several populations. Precision is indicated by area
between curves for two random subsamples, each consisting of 50 % of the data (Source:
Agterberg 1974 , Fig. 28)
and these subpopulations were plotted separately in Fig. 3.8b . The results prove that
the frequency distribution shown in Fig. 3.8a actually can be regarded as a mixture of
three separate populations with different properties. Average copper content
increases with granophyre content of gabbro in his sequence.
In order to test the stability of the separate frequency curves which are for
relatively small samples, a simple procedure for small samples originally suggested
by Mahalanobis ( 1960 ) was used by Agterberg ( 1965 ). Each sample of copper values
was randomly divided into two subsamples. For example, if there are 52 values as for
gabbro, two subsamples of 26 values were formed and plotted separately (Fig. 3.8b ).
The area between the two frequency curves for the subsamples represents the
so-called “error-area” of the curve for a combined sample. Mahalanobis ( 1960 )had
developed an approximate chi-square test based on the error-areas to test for the
separation between populations. In this application, the copper distribution for
granophyric gabbro differs signi￿cantly from those of the other two rock types.