Parameter Estimation and Measurement of Social Inequality in a Kinetic Model for Wealth Distribution

Abstract

This paper deals with the modeling of wealth distribution considering a society with non-constant population and non-conservative wealth trades. The modeling approach is based on the kinetic theory of active particles, where individuals are distinguished by a scalar variable (the activity) which expresses their social state. A qualitative analysis of the model focusing on asymptotic behaviors and measurement of inequality through the Gini coefficient is presented. Finally, some specific case-studies are proposed in order to carry out numerical experiments to validate our model, characterize societies and investigate emerging behaviors.

Cherry Picking: Consumer Choices in Swarm Dynamics, Considering Price and Quality of Goods

“…The KTAP has been applied to model several socio-economic phenomena, among others, propagation of opinion formation and credit risk over networks [6,7], idiosyncratic learning [8], opinion dynamics [9,10] and social inequality [11], while additional bibliography is provided in [12]. Another example about the use of kinetic theory to explain the market mechanisms is in [13] where the microscopic description leads to a system of linear Boltzmann-type equations.…”

Stochastic orders of log-epsilon-skew-normal distributions

“…For introduction in the field, we recommend the reader more recent books (see, for instance Shaked and Shanthikumar (2007) and Levy (2015)). Recent results regarding Gini index were given by: Zbaganu (2020) analized Loenz order and Gini index for a recent model, Preda and Catana (2021) gave theoretical results for different stochastic orders of a log-scale-location family which uses Tsallis statistics functions and results which describe the inequalities of moments or Gini index according to parameters, Buffa et al (2020) analized the inequality of the Gini coefficient in the case of a kinetic model for Wealth distribution. Also, results describing the problem of stochastic orders were given by: Ortega-Jiménez et al (2021) provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings; Balakrishnan et al (2021) analized hazard rate and reversed hazard rate orders of parallel systems with components having proportional reversed hazard rates and starting devices; Catana and Raducan (2020c) gave sufficient conditions for stochastic order of multivariate uniform distributions on closed convex sets; Catana (2021a) gave theoretical results for equivalence between di erent stochastic orders of some kind multivariate Pareto distribution family; Sfetcu et al (2021) introduced a stochastic order on Awad-Varma residual entropy and studied some properties of this order, like closure, reversed closure and preservation in some stochastic models (the proportional hazard rate model, the proportional reversed hazard rate model, the proportional odds model and the record values model); Catana and Preda (2021b) proved that different orders between parameters vectors imply the hazard order and reverse hazard order between extremes order statistics of transmuted distributions; Berrendero and Cárcamo (2012) provided a new meaning to the corresponding test statistics; Nadeb and Torabi (2020) analized different stochastic comparisons in the transmuted-G family with different parameters; Ahmadi and Arghami (2001) analized some univariate stochastic orders on record values; Bancescu (2018) presented the likelihood order of some classes of statistical distributions.…”