Related papers: The Gini Index of an Integer Partition
We study analytically the change in the wealth ($x$) distribution $P(x)$ against saving propensity $\lambda$ in a closed economy, using the Kinetic theory. We estimate the Gini ($g$) and Kolkata ($k)$ indices by deriving (using $P(x)$) the…
The norm of an integer partition is defined as the product of its parts. This statistic was recently introduced by Schneider in connection to partition zeta functions. In this note, we use the method of moments to study the distribution of…
The Gini coefficient, a non-parametric measure of galaxy morphology, has recently taken up an important role in the automated identification of galaxy mergers. I present a critical assessment of its stability, based on a comparison of…
We consider a simple theoretical model to investigate the impact of inheritances on the wealth distribution. Wealth is described as a finite resource, which remains constant over different generations and is divided equally among offspring.…
The centrality of a node within a network, however it is measured, is a vital proxy for the importance or influence of that node, and the differences in node centrality generate hierarchies and inequalities. If the network is evolving in…
This paper studies a class of rank-based inequality measures built from linear combinations of expected order statistics. The proposed framework unifies several well-known indices, including the classical Gini coefficient, the $m$th Gini…
This paper presents findings from a web-experiment on a representative sample of the French population. It examines the acceptability of the Pigou-Dalton principle of transfers, which posits that transferring income from an individual to a…
We consider strategy proof mechanisms for facility location which maximize equitability between agents. As is common in the literature, we measure equitability with the Gini index. We first prove a simple but fundamental impossibility…
We investigate the arithmetic-harmonic inequality (AHI) index, a bounded and scale-invariant measure of dispersion for positive random variables, defined through the interplay between the mean and its reciprocal. We derive analytical…
Composite indices like the Gender Equality Index (GEI) are widely used to monitor gender disparities and guide evidence-based policy. However, their original design is often limited when applied to subnational contexts. Building on the GEI…
In this paper, we propose two new flexible Gini indices (extended lower and upper) defined via differences between the $i$-th observation, the smallest order statistic, and the largest order statistic, for any $1 \leqslant i \leqslant m$.…
The categorical Gini correlation is an alternative measure of dependence between a categorical and numerical variables, which characterizes the independence of the variables. A nonparametric test for the equality of K distributions has been…
We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini correlation is interpreted as the ratio of the between-group variation and the total…
We propose a new covariance matrix called Gini covariance matrix (GCM), which is a natural generalization of univariate Gini mean difference (GMD) to the multivariate case. The extension is based on the covariance representation of GMD by…
Rand (1971) proposed what has since become a well-known index for comparing two partitions obtained on the same set of units. The index takes a value on the interval between 0 and 1, where a higher value indicates more similar partitions.…
We introduce an iterative discrete information production process where we can extend ordered normalised vectors by new elements based on a simple affine transformation, while preserving the predefined level of inequality, G, as measured by…
This papers aims to establish the empirical relationship between income, net wealth and their joint distribution in a selected group of euro area countries. I estimate measures of dependence between income and net wealth using a…
We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential…
The Wiener index of a finite graph G is the sum over all pairs (p, q) of vertices of G of the distance between p and q. When P is a finite poset, we define its Wiener index as the Wiener index of the graph of its Hasse diagram. In this…
The Boltzmann-Shannon Index (BSI) for clustered continuous data is introduced as a normalized measure that captures the relationship between geometry-based and frequency-based probability distributions defined over the clusters. In essence,…