一种新的Shannon熵估计及其在正态分布拟合优度检验中的应用

M. Madukaife
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引用次数: 0

摘要

本文基于窗口大小间隔,得到了随机变量X具有概率密度函数\(\mathit{f}\) (\(\mathit{x}\))的Shannon熵的一个新的估计量。在标准正态分布、标准指数分布和均匀分布下,通过在样本量为10、20和30时的广泛模拟研究,表明估计量具有相对低的偏差和低RMSE。基于结果,推荐它作为一个很好的熵估计。并将新估计量应用于正态性拟合优度检验。该统计量具有仿射不变性和一致性,是评价数据集单变量正态性的良好统计量。
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A New Estimator of Shannon Entropy with Application to Goodness-of-Fit Test to Normal Distribution
In this paper, a new estimator of the Shannon entropy of a random variable X having a probability density function \(\mathit{f}\)(\(\mathit{x}\)) is obtained based on window size spacings. Under the standard normal, standard exponential and uniform distributions, the estimator is shown to have relative low bias and low RMSE through extensive simulation study at sample sizes 10, 20, and 30. Based on the results, it is recommended as a good estimator of the entropy. Also, the new estimator is applied in goodness-of-fit test to normality. The statistic is affine invariant and consistent and the results show that it is a good statistic for assessing univariate normality of datasets.
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