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姓名 周宗翰(Tsung-han Chou)  查詢紙本館藏   畢業系所 數學系
論文名稱 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)
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摘要(中) 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。
摘要(英) 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.
關鍵字(中) ★ 經驗分布
★ 密度函數估計式
★ 冪數
★ 穩定型分布
關鍵字(英) ★ stable distributions
★ empirical distributions
★ kernel density estimators
★ exponent
論文目次 摘要 i
Abstract ii
l
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[4] R. A. Doney(1987). On Wiener-Hopf Factorisation and the Distribution of Extrema for Certain Stable Processes, The Annals of Probability. Volume 15, Number 4, 1352-1362.
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指導教授 許玉生(Yu-sheng Hsu) 審核日期 2007-7-17
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