对称稳定分布样本峰度行为的实证研究

IF 0.4 Q4 STATISTICS & PROBABILITY

SOUTH AFRICAN STATISTICAL JOURNAL Pub Date : 2018-11-01 DOI:10.37920/sasj.2020.54.2.9

J. M. Zyl

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引用次数: 0

摘要

峰度被视为观测数据和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，以研究当应用于不存在4阶矩的重尾数据时，峰度的样本估计相对于样本大小和尾指数的行为。研究将集中在对称稳定分布的样本上。发现过量峰度除以样本量的期望值对于尾部指数的任何值都是有限的，并且峰度的样本估计值作为样本量和尾部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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An empirical study of the behaviour of the sample kurtosis in samples from symmetric stable distributions

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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来源期刊

SOUTH AFRICAN STATISTICAL JOURNAL STATISTICS & PROBABILITY-

CiteScore

0.30

自引率

0.00%

发文量

期刊介绍： The journal will publish innovative contributions to the theory and application of statistics. Authoritative review articles on topics of general interest which are not readily accessible in a coherent form, will be also be considered for publication. Articles on applications or of a general nature will be published in separate sections and an author should indicate which of these sections an article is intended for. An applications article should normally consist of the analysis of actual data and need not necessarily contain new theory. The data should be made available with the article but need not necessarily be part of it.