摘要翻译：
讨论了金融市场中交易持续时间和首次通过过程的可能分布。提出了更新理论的观点。为了表示持续时间相对较长的市场数据，使用了两种类型的分布，即由所谓的Mittag-Leffler生存函数导出的分布和Weibull分布。对于Mittag-Leffler型分布，平均等待时间（剩余寿命）强烈地依赖于一个截止参数t_max的选择，而基于Weibull分布的结果不依赖于这样一个截止参数。因此，如果人们希望评估金融市场中的相关统计数据，如长时间的平均等待时间，威布尔分布比Mittag-Leffler分布更方便。另一方面，我们发现基尼系数与截止参数是相当独立的。基于以上考虑，我们提出了一个很好的描述市场中首次通过时间分布的候选模型：幂律尾Weibull分布。这种分布比简单的威布尔分布更有效地弥补了理论和实证结果之间的差距。我们还给出了一个确定最优交叉点的公式，使经验平均等待时间与更新理论预测的平均等待时间之差最小。此外，我们将我们的分布应用于BTP未来的分析和平均等待时间的计算，讨论了我们的分布的局限性。我们发现我们的分布是适用的，只要持续时间遵循一个Weibull定律短时间和没有太大的尾巴。
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英文标题：
《The distribution of first-passage times and durations in FOREX and
  future markets》
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作者：
Naoya Sazuka, Jun-ichi Inoue, Enrico Scalas
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最新提交年份：
2008
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Trading and Market Microstructure        交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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英文摘要：
  Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely, a distribution derived from the so-called Mittag-Leffler survival function and the Weibull distribution. For Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter t_ max, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type one if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other side, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results much more efficiently than a simple Weibull distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull-law for short times and do not have too heavy a tail.
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PDF链接：
https://arxiv.org/pdf/0808.0372