arXiv subjects

Barbara Żogała-Siudem

Publications and source records attributed to Barbara Żogała-Siudem.

4 recordsLinked to original sources

arXiv2026

Equivalence of inequality indices in the three-dimensional model of informetric impact

Inequality is an inherent part of our lives: we see it in the distribution of incomes, talents, citations, to name a few. However, its intensity varies across environments: there are systems where the available resources are relatively evenly distributed but also where a small group of items or agents controls the majority of assets. Numerous indices for quantifying the degree of inequality have been proposed but in general, they work quite differently. We recently observed (Siudem et al., 2020) that many rank-size distributions might be approximated by a time-dependent agent-based model involving a mixture of preferential (rich-get-richer) and accidental (sheer chance) attachment. In this paper, we point out its relationship to an iterative process that generates rank distributions of any length and a predefined level of inequality, as measured by the Gini index. We prove that, under our model, the Gini, Bonferroni, De Vergottini, and Hoover indices are equivalent for samples of similar sizes. Given one of them, we can recreate the value of another measure. Thanks to the obtained formulae, we can also understand how they depend on the sample size. An empirical analysis of a large database of citation records in economics (RePEc) yields a good match with our theoretical derivations.

physics.soc-ph↗

arXiv2026

The Price-Pareto growth model of networks with community structure

We introduce a new analytical framework for modelling degree sequences in individual communities of real-world networks, e.g., citations to papers in different fields. Our work is inspired by a recent modification of the Price's model, which assumes that citations are gained partly accidentally, and to some extent preferentially. Our work addresses the need to represent the heterogeneity of various scientific domains, as standard homogeneous models fail to capture the distinct growth ratios and citing cultures of different fields. Extending the model to networks with a community structure allows us to devise the analytical formulae for, amongst others, citation counts in each cluster and their inequality as described by the Gini index. We also show that a citation count distribution in each community tends to a Pareto type II distribution. Thanks to the derived model parameter estimators, the new model can be fitted to real citation and similar networks.

physics.soc-ph↗

arXiv2024

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution

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 the Gini index. Then, we derive the family of empirical Lorenz curves of the corresponding vectors and prove that it is stochastically ordered with respect to both the sample size and G which plays the role of the uncertainty parameter. We prove that asymptotically, we obtain all, and only, Lorenz curves generated by a new, intuitive parametrisation of the finite-mean Pickands' Generalised Pareto Distribution (GPD) that unifies three other families, namely: the Pareto Type II, exponential, and scaled beta distributions. The family is not only totally ordered with respect to the parameter G, but also, thanks to our derivations, has a nice underlying interpretation. Our result may thus shed a new light on the genesis of this family of distributions. Our model fits bibliometric, informetric, socioeconomic, and environmental data reasonably well. It is quite user-friendly for it only depends on the sample size and its Gini index.

physics.soc-ph↗

arXiv2015

Agent-based model for the h-index - Exact solution

The Hirsch's $h$-index is perhaps the most popular citation-based measure of the scientific excellence. In 2013 G. Ionescu and B. Chopard proposed an agent-based model for this index to describe a publications and citations generation process in an abstract scientific community. With such an approach one can simulate a single scientist's activity, and by extension investigate the whole community of researchers. Even though this approach predicts quite well the $h$-index from bibliometric data, only a solution based on simulations was given. In this paper, we complete their results with exact, analytic formulas. What is more, due to our exact solution we are able to simplify the Ionescu-Chopard model which allows us to obtain a compact formula for $h$-index. Moreover, a simulation study designed to compare both, approximated and exact, solutions is included. The last part of this paper presents evaluation of the obtained results on a real-word data set.

physics.soc-ph↗