# Seasonal Entropy, Diversity and Inequality Measures of Submitted and Accepted Papers Distributions in Peer-Reviewed Journals

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School of Business, College of Social Sciences, Arts, and Humanities, University of Leicester, Leicester LE2 1RQ, UK

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Department of Statistics and Econometrics, Bucharest University of Economic Studies, Calea Dorobantilor 15-17, 010552 Sector 1 Bucharest, Romania

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Group of Researchers for Applications of Physics in Economy and Sociology (GRAPES), Rue de la belle jardinière, 483, Angleur, B-4031 Liège, Belgium

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Institute for the Application of Nuclear Energy (INEP), University of Belgrade, 11080 Belgrade, Serbia

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Institute of Chemistry, Technology and Metallurgy, Department of Electrochemistry, University of Belgrade, 11000 Belgrade, Serbia

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Author to whom correspondence should be addressed.

Received: 29 March 2019 / Revised: 26 May 2019 / Accepted: 27 May 2019 / Published: 4 June 2019

This paper presents a novel method for finding features in the analysis of variable distributions stemming from time series. We apply the methodology to the case of submitted and accepted papers in peer-reviewed journals. We provide a comparative study of editorial decisions for papers submitted to two peer-reviewed journals: the Journal of the Serbian Chemical Society (JSCS) and this MDPI Entropy journal. We cover three recent years for which the fate of submitted papers—about 600 papers to JSCS and 2500 to Entropy—is completely determined. Instead of comparing the number distributions of these papers as a function of time with respect to a uniform distribution, we analyze the relevant probabilities, from which we derive the information entropy. It is argued that such probabilities are indeed more relevant for authors than the actual number of submissions. We tie this entropy analysis to the so called diversity of the variable distributions. Furthermore, we emphasize the correspondence between the entropy and the diversity with inequality measures, like the Herfindahl-Hirschman index and the Theil index, itself being in the class of entropy measures; the Gini coefficient which also measures the diversity in ranking is calculated for further discussion. In this sample, the seasonal aspects of the peer review process are outlined. It is found that the use of such indices, non linear transformations of the data distributions, allow us to distinguish features and evolutions of the peer review process as a function of time as well as comparing the non-uniformity of distributions. Furthermore, t- and z-statistical tests are applied in order to measure the significance (p-level) of the findings, that is, whether papers are more likely to be accepted if they are submitted during a few specific months or during a particular “season”; the predictability strength depends on the journal.