Abstract
BackgroundThe evaluation of the complexity of an observed object is an old but outstanding problem. In this paper we are tying on this problem introducing a measure called statistic complexity.Methodology/Principal FindingsThis complexity measure is different to all other measures in the following senses. First, it is a bivariate measure that compares two objects, corresponding to pattern generating processes, on the basis of the normalized compression distance with each other. Second, it provides the quantification of an error that could have been encountered by comparing samples of finite size from the underlying processes. Hence, the statistic complexity provides a statistical quantification of the statement ‘ is similarly complex as ’.ConclusionsThe presented approach, ultimately, transforms the classic problem of assessing the complexity of an object into the realm of statistics. This may open a wider applicability of this complexity measure to diverse application areas.
Highlights
Complex systems is the study of interactions of simple building blocks that result in a collective behavior or properties absent in the elementary components of the system itself
The presented approach, transforms the classic problem of assessing the complexity of an object into the realm of statistics. This may open a wider applicability of this complexity measure to diverse application areas
The purpose of this paper is to introduce a new measure of complexity we call statistic complexity that is different to all other complexity measures introduced so far, and connects directly to statistics, to statistical inference [25,26]
Summary
Complex systems is the study of interactions of simple building blocks that result in a collective behavior or properties absent in the elementary components of the system itself. Properties or characteristics of a multitude of different complex systems from these fields has been studied to date [6,7,8], the complexity of an object may have received the most attention. This property of complex systems has fascinated generations of scientists [9,10,11] trying to quantify such a notation. In this paper we are tying on this problem introducing a measure called statistic complexity
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