Random sets and histograms

Abstract

One of the main reasons why histograms are the most used density estimators is that they are easier to implement and interpret than other density estimators. Some people have already exploited the connection between probability theory and possibility theory or fuzzy sets to set up membership functions and to create fuzzy sets models. Two different ways have been used: 1) transform the density function of a random variable into a possibility measure, which is an almost automatic operation; and 2) calculate the coverage function of a random set, which is a possibility measure. In this paper, we show that a histogram is the coverage function of a determined random set. This suggests other methods to create more accurate or different featured histograms by using the random set theory. One example of a histogram with overlapping classes is provided.