Scale curve – a robust and nonparametric approach to study a dispersion and interdependence of multivariate distributions

A scale curve is a nonparametric approach to study a dispersion of a random vector around a multivariate median. The scale curve is a volume functional based on probabilities allocated on the so-called central regions induced by a given statistical depth function. The curve expresses a degree of dispersion of random vector in a central regions expansion categories. We can also use the curve to display a degree of interdependence of marginal components of a specific distribution. In this paper we discuss selected theoretical aspects of the scale curve induced by a projection depth function. We study the performance of the propositions on various multivariate data sets simulated from skewed, fat tailed and including outliers distributions.