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Random sets and histograms

Authors: Javier Nunez-Garcia; Olaf Wolkenhauer;

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.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
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