Ana G. Elias | Searcharxiv

arXiv2026

A Systematic Comparison of q-Gaussian Fitting Methods across Complex Systems

Nature exhibits a wide variety of nonlinear phenomena characterized by strong fluctuations that push the system away from equilibrium. Recent studies have shown that non-extensive statistics are more suitable for analyzing these phenomena, as they can capture long-range correlations and heavy-tailed distributions that conventional Boltzmann-Gibbs statistics cannot represent. However, estimating the non-extensiveness parameter ($q$) is not trivial, and methods vary significantly across disciplines. This paper presents a systematic and interdisciplinary comparison of three fitting methods: direct nonlinear fitting of the probability distribution function (PDF), linearization using the q-logarithm function, and numerical fitting of the cumulative distribution function (CDF). We applied this analysis to various phenomena, from areas such as geophysics, space weather and economics, analyzing the critical impact of discretization. The results show that $q$ estimates are highly sensitive to histogram binning, while the CDF-based method provides a bin-free alternative that yields more stable estimates for the datasets analyzed here. This contribution provides relevant information for the search for a method that allows the correct determination of the parameters of heavy-tailed distributions in various disciplines.

cond-mat.stat-mech↗

arXiv2021

How much has the Sun influenced Northern Hemisphere temperature trends? An ongoing debate

To evaluate the role of Total Solar Irradiance (TSI) on Northern Hemisphere (NH) surface air temperature trends it is important to have reliable estimates of both quantities. 16 different TSI estimates were compiled from the literature. 1/2 of these estimates are low variability and 1/2 are high variability. 5 largely-independent methods for estimating NH temperature trends were evaluated using: 1) only rural weather stations; 2) all available stations whether urban or rural (the standard approach); 3) only sea surface temperatures; 4) tree-ring temperature proxies; 5) glacier length temperature proxies. The standard estimates using urban as well as rural stations were anomalous as they implied a much greater warming in recent decades than the other estimates. This suggests urbanization bias might still be a problem in current global temperature datasets despite the conclusions of some earlier studies. Still, all 5 estimates confirm it is currently warmer than the late 19th century, i.e., there has been some global warming since 1850. For the 5 estimates of NH temperatures, the contribution from direct solar forcing for all 16 estimates of TSI was evaluated using simple linear least-squares fitting. The role of human activity in recent warming was then calculated by fitting the residuals to the UN IPCC's recommended anthropogenic forcings time series. For all 5 NH temperature series, different TSI estimates implied everything from recent global warming being mostly human-caused to it being mostly natural. It seems previous studies (including the most recent IPCC reports) that had prematurely concluded the former failed to adequately consider all the relevant estimates of TSI and/or to satisfactorily address the uncertainties still associated with NH temperature trend estimates. Several recommendations are provided on how future research could more satisfactorily resolve these issues.

physics.ao-ph↗