An alternative approach to the median of a random interval using an L 2 metric

Abstract

Since the Aumann-type expected value of a random interval is not robust, the aim of this paper is to propose a new central tendency measure for interval-valued data. The median of a random interval has already been defined as the interval minimizing the mean distance, in terms of an L1 metric extending the Euclidean distance, to the values of the random interval. Inspired by the spatial median, we now follow a more common approach to define the median using an L2 metric. © 2013 Springer-Verlag.