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 Scope All of NCUIR 理學院    數學研究所       --博碩士論文 Tips: please add "double quotation mark" for query phrases to get precise resultsplease goto advance search for comprehansive author search Adv. Search
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 Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7918

 Title: 單峰穩定型分布之冪數的經驗分布及核密度函數估計法;Exponent Estimations for Unimodal Stable Distribution based on Empirical Distributions and Kernel Density Estimators Authors: 周宗翰;Tsung-han Chou Contributors: 數學研究所 Keywords: 經驗分布;密度函數估計式;冪數;穩定型分布;stable distributions;empirical distributions;kernel density estimators;exponent Date: 2007-07-05 Issue Date: 2009-09-22 11:09:03 (UTC+8) Publisher: 國立中央大學圖書館 Abstract: 穩定型分布之冪數因未出現於密度函數或分布函數，故不易估計，本文介紹一些估計冪數的方法。我們發現，單峰穩定型分布之冪數為密度函數或分布函數之泛函，故可由核密度函數估計式或經驗分布估計之。我們將討論這些估計式的性質及應用。 The collection of stable distributions is a particular class of distributions studied in probability and statistics. Let \$X,X_1,ldots,X_k\$ denote a sequence of i.i.d. random variables with a common distribution \$R\$. If for all positive integer \$k\$, \$X\$ and \$frac{X_1+cdots+X_k}{k^alpha}\$ have the same distribution for some constant \$alpha\$, then \$R\$ is a stable distribution with exponent \$frac{1}{alpha}\$. It is difficult to estimate exponent \$alpha\$ since \$alpha\$ does not appear in probability density function. The purpose of this paper is to study some estimators of \$alpha\$ and their applications. We find that under unimodal assumption \$alpha\$ is a functional of probability density function or distribution function. Consequently, \$alpha\$ can be estimated by kernel density estimators or empirical distributions. Appears in Collections: [數學研究所] 博碩士論文

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