Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders

Vasile Preda and Luigi-Ionut Catana
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Vasile Preda: “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie Street, 050711 Bucharest, Romania
Luigi-Ionut Catana: Faculty of Mathematics and Computer Science, Mathematical Doctoral School, University of Bucharest, Str. Academiei nr. 14, Sector 1, 010014 Bucharest, Romania

Mathematics, 2021, vol. 9, issue 11, 1-22

Abstract: In this article we give theoretical results for different stochastic orders of a log-scale-location family which uses Tsallis statistics functions. These results describe the inequalities of moments or Gini index according to parameters. We also compute the mean in the case of q-Weibull and q-Gaussian distributions. The paper is aimed at analyzing the order between survival functions, Lorenz curves and (as consequences) the moments together with the Gini index (respectively a generalized Gini index). A real data application is presented in the last section. This application uses only the survival function because the stochastic order implies the order of moments. Given some supplementary conditions, we prove that the stochastic order implies the Lorenz order in the log-scale-location model and this implies the order between Gini coefficients. The application uses the estimated parameters of a Pareto distribution computed from a real data set in a log-scale-location model, by specifying the Kolmogorov–Smirnov p -value. The examples presented in this application highlight the stochastic order between four models in several cases using survival functions. As direct consequences, we highlight the inequalities between the moments and the generalized Gini coefficients by using the stochastic order and the Lorenz order.

Keywords: Gini index; Tsallis statistics; stochastic orders (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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