修正累积分布函数在CTRW场景下等待时间分析中的应用
Modified cumulative distribution function in application to waiting time analysis in CTRW scenario
摘要：
连续时间随机游走模型在模拟所谓的反常扩散行为中起着重要的作用。这种模型的具体属性之一是在轨迹中可见的恒定时间段。在连续时间随机游走方法中，它们是称为等待时间的序列的实现。本文的重点是分析等待时间的分布。我们在这里介绍新的方法估计和统计调查，这样的分布。该方法基于修正的累积分布函数。本文考虑了等待时间分布的三种特殊情况，即$α$ -稳定、回火稳定和伽玛分布。然而，所提出的方法可以应用于广泛的分布集-一般来说，它可以作为拟合任何分布函数的方法，如果观察结果被舍入。新的统计技术，我们适用于模拟数据以及描述室内空气中的$CO_2$浓度的真实数据。
英文摘要：
The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random walk approach they are realizations of the sequence called waiting times. The main attention of the paper is paid on the analysis of waiting times distribution. We introduce here novel methods of estimation and statistical investigation of such distribution. The methods are based on the modified cumulative distribution function. In this paper we consider three special cases of waiting time distributions, namely $α$-stable, tempered stable and gamma. However the proposed methodology can be applied to broad set of distributions - in general it may serve as a method of fitting any distribution function if the observations are rounded. The new statistical techniques we apply to the simulated data as well as to the real data describing $CO_2$ concentration in indoor air.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
