Interval Compositional Data: Problems and Possibilities

Abstract

In statistics, compositional data are defined as multivariate observations that quantitatively describe contributions of parts on a whole, carrying exclusively relative information. As a consequence, compositions can be represented as proportions or percentages without loss of information (contained in ratios between parts). Nevertheless, in the practice parts of compositional data are frequently formed by intervals; for example, concentrations of chemical elements are provided not as exact numbers, but rather in an interval range. Intuitively, a natural question arises, whether the relative information is preserved, when the original compositional data with interval-valued parts are represented in proportions. Namely, from the arithmetic properties of interval data, normalizing of intervals does not simply follow the case of real values, but a special procedure according to constrained interval arithmetic is needed. The aim of the contribution is to discuss possibilities of representing the interval compositional data in proportions.