κ-generalized models of income and wealth distributions: A survey

Abstract

The paper provides a survey of results related to the "κ-generalized distribution", a statistical model for the size distribution of income and wealth. Topics include, among others, discussion of basic analytical properties, interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution field, such as the Gini index and the Lorenz curve. An extension of the basic model that is most able to accommodate the special features of wealth data is also reviewed. The survey of empirical applications given in this paper shows the κ-generalized models of income and wealth to be in excellent agreement with the observed data in many cases.

Jeans gravitational instability with κ-deformed Kaniadakis distribution in Eddington-inspired Born–Infield gravity*

“…Among them, the κ-deformed Kaniadakis distribution, one of the more general distribution functions, [30] has been established by Kaniadakis [29] in 2001 and developed over the past decades, which is now widely applied to the field of black-body radiation, [31] quantum entanglement, [32] cosmic rays, [33] plasma physics, [34,35] kinetics of interaction atoms and photons, [36] nonlinear kinetics, [37,38] and even the financial systems, [39] etc. It should be point out that some studies recently have used the κ-deformed distribution to examine the Jeans instability of self-gravitational systems and showed that it plays a significant role in the process of gravitating collapse of matter systems.…”

SYNC: A Copula based Framework for Generating Synthetic Data from Aggregated Sources

“…First of all, our method relies on Gaussian copulae and this can be further extended by leveraging other families of copula models to better model the underlying dependency structures. Secondly, we use beta and log-normal distributions to approximate marginal distributions for categorical and continuous variables, respectively, and other families of distributions could be considered (e.g., the κ-generalized model [30] can be used for money related distributions). Lastly, a better similarity metric can be designed to assess generated data against its original input.…”

Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries

“…The existence of a mode when y tends to zero, regardless of whether the distribution presents another within its range, is a specific advantage of this distribution compared to the most widely used and best models for fitting empirical income distributions 3 . In the section on parameter estimation and goodness of fit measures, we compare the log t distribution to the Singh-Maddala, the κ-generalized model, the Dagum type I, the lognormal distribution and the generalized beta of the second kind (GB2), which only present a unique mode, either at zero or inside its range (see, among others, Boccafuso et al, 2013, Bandourian et al, 2002, Callealta et al, 1997and Clementi et al, 2006.…”