Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario
Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario
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DOI：
10.1088/1751-8121/50/3/034002
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
R. Połoczański;A. Wyloma'nska;M. Maciejewska;A. Szczurek;J. Gajda
中科院分区：
文献类型：
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作者：
R. Połoczański;A. Wyloma'nska;M. Maciejewska;A. Szczurek;J. Gajda
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。这种模型的一个具体属性是在轨迹中出现恒定的时间段。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。在这项工作中，我们专注于分析的等待时间分布，引入新的方法，参数估计和统计调查这样的分布。这些方法都是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-稳定分布、回火稳定分布和γ-稳定分布。然而，所提出的方法可以适用于广泛的分布，一般来说，它可以作为一种方法来拟合任何分布函数，如果观察四舍五入。将新的统计技术应用于室内空气中CO2浓度的模拟数据以及真实的数据。
The continuous time random walk model plays an important role in modelling of the so-called anomalous diffusion behaviour. One of the specific properties of such model is the appearance of constant time periods in the trajectory. In the continuous time random walk approach they are realizations of the sequence called waiting times. In this work we focus on the analysis of waiting time distribution by introducing novel methods of parameter estimation and statistical investigation of such a distribution. These 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 are applied to the simulated data as well as to the real data of CO2 concentration in indoor air.