Probability and Statistics - Geomathematics: Theoretical Foundations, Applications and Future Developments - page 61

Fig. 2.5 Frequency curve ( 3 ) for the sum of a rectangular distribution ( 1 ) and a Gaussian
distribution ( 2 ). This kind of frequency distribution results from random sampling of a space- or
time-variable subject to a linear trend changing from 0 to 5 in this artificial example. Residuals
from the trend have zero mean and unity variance. The three curves have areas equal to one
(Source: Agterberg 1974 , Fig. 23)

on derivation of the equation for the curve g ( x ) in Fig. 2.5 are given in Agterberg
( 1974 , pp. 195-198). In the next chapter the model will be used for maximum
likelihood estimation of the age of stage boundaries in the Geologic Timescale.
It also will be used as a partial explanation of the Vistelius lognormality model
( cf . Sect. 3.2 ).

2.4 Applications of Statistical Analysis

As shown by Schuenemeyer and Drew ( 2011 ), many problems of mathematical
geoscience are best solved by using the methods of classical statistics. The aim of
the next example is to apply statistical inference ( F -, t - and

2 - tests) to a set of age
data to be followed by a graphical ( Q - Q ) test applied to solve the same problem.

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2.4.1 Statistical Inference: Grenville
Potassium/Argon Ages Example

The normal distribution can be used as a starting point for various types of
significance tests: notably Student's t -test, the chi-square test and the F -test in
analysis of variance. Usage of these tests is illustrated on the basis of age data that
were available in 1968 for the Grenville Province on the Canadian Shield