英文标题：
《An Empirical Study of the Behaviour of the Sample Kurtosis in Samples
  from Symmetric Stable Distributions》
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作者：
J. Martin van Zyl
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最新提交年份：
2018
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英文摘要：
  Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample estimate of kurtosis with respect to sample size and the tail index when applied to heavy-tailed data where the 4th moment does not exist. The study will focus on samples from the symmetric stable distributions. It was found that the expected value of excess kurtosis divided by the sample size is finite for any value of the tail index and the sample estimate of kurtosis increases as a linear function of sample size and tail index. It is very sensitive to changes in the tail-index.
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中文摘要：
峰度被视为观测数据与高斯分布之间差异的度量，并在第四矩有限时定义。在这项工作中，进行了一项实证研究，以调查当应用于不存在四阶矩的重尾数据时，峰度样本估计相对于样本量和尾部指数的行为。这项研究将集中于对称稳定分布的样本。研究发现，对于尾指数的任何值，剩余峰度的期望值除以样本量都是有限的，并且峰度的样本估计随着样本量和尾指数的线性函数而增加。它对尾部指数的变化非常敏感。
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分类信息：

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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