Related papers: On a property of the inequality curve $\lambda(p)$
In this article we will prove that if the continuous closed curve $\gamma : [0, 1] \rightarrow \mathbb{R}^2$ has finite $p$-variation with $p < 2$, then $(\iint\limits_{\mathbb{R}^2}|\eta(\gamma, (x, y))|^q \,dx \,dy)^{1/q} \le…
The aim of this note is twofold. Firstly, we prove an abstract version of the Calder\'on transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does…
We introduce $\zeta$- and $s$-values as quantile-based standardizations that are particularly suited for hypothesis testing. Unlike p-values, which express tail probabilities, $s$-values measure the number of semi-tail units into a…
This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities…
Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of…
At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…
To simultaneously overcome the limitation of the Gini index in that it is less sensitive to inequality at the tails of income distribution and the limitation of the inter-decile ratios that ignore inequality in the middle of income…
In this paper we derive inferential results for a new index of inequality, specifically defined for capturing significant changes observed both in the left and in the right tail of the income distributions. The latter shifts are an apparent…
We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an…
Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…
A basic result in the elementary theory of continued fractions says that two real numbers share the same tail in their continued fraction expansions iff they belong to the same orbit under the projective action of PGL(2,Z). This result was…
We study model theoretic tree properties ($\text{TP}, \text{TP}_1, \text{TP}_2$) and their associated cardinal invariants ($\kappa_{\text{cdt}}, \kappa_{\text{sct}}, \kappa_{\text{inp}}$, respectively). In particular, we obtain a…
This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching…
The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the…
Classical inequality curves and inequality measures are defined for distributions with finite mean value. Moreover, their empirical counterparts are not resistant to outliers. For these reasons, quantile versions of known inequality curves…
We prove that the split property is a stable feature for spin chain states which are related by composition with *-automorphisms generated by power-law decaying interactions. We apply this to the theory of the $\mathbb{Z}_2$-index for…
Inequality indices are quantitative scores that gauge the divergence of wealth distributions in human societies from the "ground state" of pure communism. While inequality indices were devised for socioeconomic applications, they are…
The celebrated Hardy inequality can be written in the form $$\int_0^\infty \mathcal{P}_p \big(f|_{[0,x]}\big)dx \le (1-p)^{-1/p} \int_0^\infty f(x)\:dx \qquad \text{ for }p\in(0,1)\text{ and }f \in L^1\text{ with }f\ge0,$$ where…
Accurately estimating income Pareto exponents is challenging due to limitations in data availability and the applicability of statistical methods. Using tabulated summaries of incomes from tax authorities and a recent estimation method, we…
This work analyzes the Gompertz-Pareto distribution (GPD) of personal income, formed by the combination of the Gompertz curve, representing the overwhelming majority of the economically less favorable part of the population of a country,…