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Randentropy: A Software to Measure Inequality in Random Systems
Volume 33, Issue 2 (2022), pp. 279–298
Pub. online: 22 March 2022      Type: Research Article      Open accessOpen Access
Received
1 March 2021
Accepted
1 March 2022
Published
22 March 2022

Abstract

The software Randentropy is designed to estimate inequality in a random system where several individuals interact moving among many communities and producing dependent random quantities of an attribute. The overall inequality is assessed by computing the Random Theil’s Entropy. Firstly, the software estimates a piecewise homogeneous Markov chain by identifying the change-points and the relative transition probability matrices. Secondly, it estimates the multivariate distribution function of the attribute using a copula function approach and finally, through a Monte Carlo algorithm, evaluates the expected value of the Random Theil’s Entropy. Possible applications are discussed as related to the fields of finance and human mobility.

References

 
Asadi, M., Zohrevand, Y. (2007). On the dynamic cumulative residual entropy. Journal of Statistical Planning and Inference, 137(6), 1931–1941.
 
Behrendt, S., Dimpfl, T., Peter, F.J., Zimmermann, D.J. (2019). RTransferEntropy—quantifying information flow between different time series using effective transfer entropy. SoftwareX, 10, 100265.
 
Calì, C., Longobardi, M., Navarro, J. (2020). Properties for generalized cumulative past measures of information. Probability in the Engineering and Informational Sciences, 34(1), 92–111.
 
Curiel, R.P., Bishop, S. (2016). A measure of the concentration of rare events. Scientific Reports, 6, 32369.
 
D’Amico, G., Di Biase, G. (2010). Generalized concentration/inequality indices of economic systems evolving in time. Wseas Transactions on Mathematics, 9(2), 140–149.
 
D’Amico, G., Di Biase, G., Manca, R. (2012). Income inequality dynamic measurement of Markov models: application to some European countries. Economic Modelling, 29(5), 1598–1602.
 
D’Amico, G., Di Biase, G., Manca, R. (2014). Decomposition of the population dynamic Theil’s entropy and its application to four european countries. Hitotsubashi Journal of Economics, 55(2), 229–239.
 
D’Amico, G., Di Biase, G., Janssen, J., Manca, R. (2017). Semi-Markov Migration Models for Credit Risk. John Wiley & Sons.
 
D’Amico, G., Scocchera, S., Storchi, L. (2018a). Financial risk distribution in European Union. Physica A: Statistical Mechanics and its Applications, 505, 252–267.
 
D’Amico, G., Regnault, P., Scocchera, S., Storchi, L. (2018b). A continuous-time inequality measure applied to financial risk: the case of the European Union. International Journal of Financial Studies, 6(3), 62.
 
D’Amico, G., Petroni, F., Regnault, P., Scocchera, S., Storchi, L. (2019). A Copula-based Markov reward approach to the credit spread in the European Union. Applied Mathematical Finance, 26(4), 359–386.
 
Di Crescenzo, A., Longobardi, M. (2002). Entropy-based measure of uncertainty in past lifetime distributions. Journal of Applied probability, 39, 434–440.
 
Di Crescenzo, A., Longobardi, M. (2009). On cumulative entropies. Journal of Statistical Planning and Inference, 139(12), 4072–4087.
 
Dubois, P.F., Hinsen, K., Hugunin, J. (1996). Numerical python. Computers in Physics, 10(3), 262–267.
 
Durante, F., Sempi, C. (2016). Principles of Copula Theory, Vol. 474. CRC Press, Boca Raton, FL.
 
Ferguson, N., Datta, S., Brock, G. (2012). msSurv: an R package for nonparametric estimation of multistate models. Journal of Statistical Software, 50(14), 1–24.
 
Hunter, J.D. (2007). Matplotlib: a 2D graphics environment. Computing in Science & Engineering, 9(3), 90–95.
 
Jackson, C.H., (2011). Multi-state models for panel data: the msm package for R. Journal of Statistical Software, 38(8), 1–29.
 
Jaynes, E.T. (1957). Information theory and statistical mechanics. Physical Review, 106(4), 620.
 
Jones, E., Oliphant, T., Peterson, P. (2001). SciPy: Open source scientific tools for Python. [Online; accessed 2019-02-05]. http://www.scipy.org.
 
Król, A., Saint-Pierre, P. (2015). SemiMarkov: an R package for parametric estimation in multi-state semi-Markov models. Journal of Statistical Software, 66(6).
 
Krumme, C., Llorente, A., Cebrian, M., Moro, E. (2013). The predictability of consumer visitation patterns. Scientific Reports, 3, 1645.
 
Kullback, S., Leibler, R.A. (1951). On information and sufficiency. The Annals of Mathematical Statistics, 22(1), 79–86.
 
Marcon, E., Hérault, B. (2015a). entropart: an R package to measure and partition diversity. Journal of Statistical Software, 67(1), 1–26.
 
Marcon, E., Hérault, B. (2015b). entropart: an R package to measure and partition diversity. Journal of Statistical Software, 67(1), 1–26.
 
Phillips, S.J., Anderson, R.P., Schapire, R.E. (2006). Maximum entropy modeling of species geographic distributions. Ecological Modelling, 190(3-4), 231–259.
 
Polansky, A.M. (2007). Detecting change-points in Markov chains. Computational Statistics & Data Analysis, 51(12), 6013–6026.
 
PyQT (2012). PyQt Reference Guide. http://www.riverbankcomputing.com/static/Docs/PyQt4/html/index.html.
 
Rao, M., Chen, Y., Vemuri, B.C., Wang, F. (2004). Cumulative residual entropy: a new measure of information. IEEE Transactions on Information Theory, 50(6), 1220–1228.
 
Saad, T., Ruai, G. (2019). PyMaxEnt: a Python software for maximum entropy moment reconstruction. SoftwareX, 10, 100353.
 
Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423.
 
Song, L., Kotz, D., Jain, R., He, X. (2006). Evaluating next-cell predictors with extensive Wi-Fi mobility data. IEEE Transactions on Mobile Computing, 5(12), 1633–1649.
 
Storchi, L. (2020). MarkovTheil code. GitHub.
 
Summerfield, M. (2007). Rapid GUI Programming with Python and Qt: The Definitive Guide to PyQt Programming (paperback). Pearson Education.
 
Theil, H. (1967). Economics and information theory. Technical report.
 
Trueck, S., Rachev, S.T. (2009). Rating Based Modeling of Credit Risk: Theory and Application of Migration Matrices. Academic Press.

Biographies

D’Amico Guglielmo
g.damico@unich.it

G. D’Amico is a full professor of mathematical methods in economics, finance and insurance at the Department of Economics of the “G. D’Annunzio” University of Chieti-Pescara. He received his PhD in mathematics for applications in economics, finance and insurance from the University “La Sapienza” of Rome in May 2005. His research interests include the theory of stochastic processes and their applications in finance, insurance, economics, reliability and wind energy. He is interested also in nonparametric statistical inference for stochastic processes. His research has appeared in several refereed journals such as European Journal of Operational Research, Applied Mathematical Finance, Scandinavian Actuarial Journal, Applied Mathematical Modelling, IMA Journal of Management Mathematics, Journal of the Operational Research Society, Reliability Engineering and System Safety, Stochastics, Insurance: Mathematics and Economics. He has published a book with John Wiley and Sons.

Scocchera Stefania

S. Scocchera works in the Credit Risk Model office at Banco BPM SPA, dealing with projects concerning the Credit Portfolio Model, the inclusion of the climate risk (ESG) within risk parameters and satellite models. She received her PhD in accounting, management and finance with specialization in mathematical finance from the “G. D’Annunzio” University of Chieti-Pescara in May 2019.

Storchi Loriano
loriano@storchi.org

L. Storchi is an associate professor and after more than 15 years of research activity he has acquired wide competences in several programming languages, numerical methods and data modelling. His multidisciplinary background is reflected both in the list of his scientific interests, as well as in the diversity of his publications.


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© 2022 Vilnius University
Open access article under the CC BY license.

Keywords
random entropy Markov reward model copula change-point

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