We are pleased to announce that our paper
On the definition of median for a random interval
has been accepted for publication in Information Sciences.
This paper, written by Olaya González-Campos, Raúl Pérez-Fernández and Enrique Miranda, addresses the problem of extending the classical notion of median to set-valued observations in the context of random intervals under the epistemic interpretation. We model imprecise data arising from absolute measurement error, relative measurement error, and data rounding, providing a solid theoretical foundation for location statistics when precise observations are unavailable.
In particular, in this contribution we introduce four distinct notions of median for a random interval: the median, the extended median, the weak median, and the n-empirical median. For each of these constructs, we study their main mathematical properties and provide explicit characterizations when the lower and upper bounds of the interval are comonotone. Finally, we show how all four definitions extend naturally to general p-order quantiles and their linear combinations.