Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1507.03408

A classification of natural and social distributions Part one: the descriptions

L. Benguigui·M. Marinov
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions used to describe the distributions. The goal of the study was to determine, whether a unique function can be used to describe all the distributions (universality) or a particular function is best suited to describe the distributions in each specific field of research (domain universality). We propose a classification of distributions into eighth different categories, based on three representations: the Zipf representation, the cumulative density function (CDF) and the probability density function (PDF). In the 89 cases included in the survey, neither universality nor domain universality was found. In particular, based on the results of the survey, the claim that "power law provides a good description for majority of distributions" may be rejected. Only one third of the distributions in our survey are associated with power laws, while another third is well described by lognormal and similar functions (Dagum, Weibull, loglogistic and Gamma functions). We suggest that correct characterization of a distribution relies on two conditions. First, it is important to include the full range of the available data to avoid distortion due to arbitrary cut off values. Second, it is advisable to display the data in all three representations: the Zipf representation, the CDF and the PDF.

Explore related subjects

physics.soc-ph

Keep this discovery

BibTeXRIS

L. Benguigui, M. Marinov. 2015-07-13. A classification of natural and social distributions Part one: the descriptions. https://arxiv.org/abs/1507.03408

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Energy pathway variety and the progress of the energy transition in European countries

The integration of new energy forms into existing energy infrastructure has emerged as a critical challenge in the context of the pursuit of a sustainable energy transition. One of the main challenges is understanding how this integration takes place not only from the introduction, but also as energy follows existing paths or creates new ones through which it is transformed and used by different activities. Here we introduce techniques from network science to analyse this process for the case of 29 European countries between 1992 and 2021. We study how new energy forms increase or decrease the variety (heterogeneity) of paths through the system of each country by establishing new ones and replacing or phasing out existing ones. We find that the transition to systems based on renewable energy is characterised by an initial increase in the variety of paths while the heterogeneity of paths decreases at the end of the transition, when the proportion of non-renewables in the system tends to zero. We then demonstrate that greater heterogeneity (complexity) is associated with larger annual fluctuations in the proportion of non-renewable sources in the system, establishing a direct relationship between the progress of the transition and the complexity of the energy system in which it occurs. This contributes to the understanding of general properties of the dynamics of the energy transition and effects that accelerate or deter it.

physics.soc-ph↗
arXiv2026

Fundamental limits to identifying node and tie memory in temporal networks: marginal artefacts and spreading dynamics

Temporal-network models attribute memory in contact data to either node self-excitation (branching ratio n_node) or tie reinforcement (kappa), carrying major consequences for epidemic spreading. We prove that when event initiators are observed, the two mechanisms are orthogonal: the Fisher information is block-diagonal and neither trades off against the other. In undirected proximity data, where initiators are unobserved, marginalising over them couples the mechanisms into a structural confound that survives posterior smoothing. On empirical proximity, messaging, and email records, however, a cruder failure dominates: fitted node memory is pinned to the inter-event marginal law and remains virtually invariant across latent label posterior samples (coefficient of variation below 1%). An inter-event-order shuffle test and burstiness-memory diagnostics reveal that exponential-Hawkes node memory is recovered from none, while tie reinforcement remains identifiable throughout. This near-unidentifiability is intrinsic, not an artefact of the exponential kernel: refitting flexible scale-free (sum-of-exponentials) kernels on synthetic power-law self-exciting processes fails to distinguish genuine node memory from memoryless renewal controls, with identical collapses recurring on algorithmic networks (edit bots, cloud microservices) and cortical spiking. Downstream epidemic consequences are quantitative: simulations fitted to empirical contact records under-predict outbreak sizes by up to a factor of 2.5 and shift the epidemic threshold. We conclude that observational temporal networks face a two-fold identifiability boundary: contact directionality is essential to decouple tie reinforcement, whereas heavy-tailed node self-excitation is intrinsically unidentifiable from contact timings alone.

physics.soc-ph↗
arXiv2026

Assessing extreme flood impacts on urban rail transit: A passenger-oriented, resilience-informed framework

Urban rail transit systems (URTSs) are increasingly exposed to extreme floods following heavy precipitation, yet passenger travel impacts are often assessed through delay-based indicators that overlook infeasible journeys under large-scale disruptions. This study develops a passenger-oriented, resilience-informed framework for assessing flood impacts on URTS journeys from disruption onset to recovery completion. The framework presents a novel six-category classification of journey impacts, explicitly considering rerouting, alternative station use, and a delay threshold. It is demonstrated through hourly dynamic simulations of 15 London URTS lines under 30-year, 100-year, and 1,000-year flood risk scenarios. Results indicate that severe flood disruptions lead to substantial unsatisfied demand, driven primarily by unavailable routes rather than unacceptable delays. Compared with finer behaviour adjustments, rerouting dominates travel impacts. These findings highlight the significance of moving beyond delay-based assessment and provide valuable evidence on essential behavioural mechanisms for strategic-level stress testing intended to inform URTS flood resilience intervention planning.

physics.soc-ph↗