Deformation of power law in the double Pareto distribution using uniformly distributed observation time

IF 2.2 3区物理与天体物理 Q2 MECHANICS

Journal of Statistical Mechanics: Theory and Experiment Pub Date : 2024-04-23 DOI:10.1088/1742-5468/ad3a5c

Ken Yamamoto, Takashi Bando, Hirokazu Yanagawa and Yoshihiro Yamazaki

引用次数: 0

Abstract

The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the exponential distribution of the observation time is replaced with a continuous uniform distribution. The probability density, complementary cumulative distribution, and moments of this model are exactly calculated. Furthermore, the validity of the analytical calculations is discussed in comparison with numerical simulations of stochastic processes.

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利用均匀分布的观测时间实现双帕累托分布中幂律的变形

双帕累托分布是一种具有幂律尾部的重尾分布，它是通过几何布朗运动和指数分布的观察时间产生的。在本研究中，我们研究了一个修正模型，其中观测时间的指数分布被连续均匀分布所取代。我们精确计算了该模型的概率密度、互补累积分布和矩。此外，通过与随机过程的数值模拟进行比较，讨论了分析计算的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Statistical Mechanics: Theory and Experiment 物理-力学

CiteScore

4.50

自引率

12.50%

发文量

210

审稿时长

1.0 months

期刊介绍： JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged. The journal covers different topics which correspond to the following keyword sections. 1. Quantum statistical physics, condensed matter, integrable systems Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo 2. Classical statistical mechanics, equilibrium and non-equilibrium Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo 3. Disordered systems, classical and quantum Scientific Directors: Eduardo Fradkin and Riccardo Zecchina 4. Interdisciplinary statistical mechanics Scientific Directors: Matteo Marsili and Riccardo Zecchina 5. Biological modelling and information Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina