ABSTRACT
One can say that logratio transformations bring compositional data from the “simplex world” into the “real world”, that is into an unbounded space of real numbers where classical statistics can be applied. One consequence is that logratios might follow the normal distribution, the univariate normal for a single logratio or multivariate normal for a set of ratios. Such a possibility can have many benefits for statistical summaries and inference. This brings us directly to the topic of the lognormal distribution and its multivariate extensions, which is the subject of this chapter. The case of non-normal logratios will also be treated. This chapter can be skipped during a first reading of the book, or skipped entirely if the reader is interested only in data analytical aspects.
