AI 中文总结
本文系统比较了三种q-高斯拟合方法，发现CDF数值拟合对$q$的估计更稳定，为各学科重尾分布参数确定提供了参考。
AI 中文摘要
自然界呈现出各种强波动的非线性现象，这些现象使系统远离平衡态。近期研究表明，非广延统计更适合分析这些现象，因为它能捕捉传统玻尔兹曼-吉布斯统计无法表示的长程关联和重尾分布。然而，估计非广延参数（$q$）并非易事，且不同学科的方法差异显著。本文对三种拟合方法开展了系统的跨学科比较：概率分布函数（PDF）的直接非线性拟合、利用q-对数函数的线性化、累积分布函数（CDF）的数值拟合。我们将该分析应用于地球物理学、空间天气学和经济学等领域的多种现象，分析了离散化的关键影响。结果显示，$q$的估计对直方图分箱高度敏感，而基于CDF的方法提供了一种无分箱的替代方案，能为本文分析的数据集产生更稳定的估计。本研究为各学科中重尾分布参数的正确确定方法的探索提供了相关信息。
英文摘要
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.
Comments10 pages, 9 figures
