A Critical Approach to Probability Laws in Geochemistry

Abstract

Probability laws in geochemistry have been a major issue of concern over the last decades. The lognormal on the positive real line or the additive logistic normal on the simplex are two classical laws of probability to model geochemical data sets due to their association with a relative measure of difference. This fact is not fully exploited in the classical approach when viewing both the positive real line and the simplex as subsets of real space with the induced geometry. But it can be taken into account considering them as real linear vector spaces with their own structure. This approach implies using a particular geometry and a measure different from the usual ones. Therefore, we can work with the coordinates with respect to an orthonormal basis. It could be shown that the two mentioned laws are associated with a normal distribution on the coordinates. In this contribution both approaches are compared, and a real data set is used to illustrate similarities and differences.