穩定型分布之冪數之倒數的點估計; Estimations for Inverse of Exponents of Stable Distributions

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7968

Title:	穩定型分布之冪數之倒數的點估計;Estimations for Inverse of Exponents of Stable Distributions
Authors:	蘇健霖;Chien-Lin Su
Contributors:	數學研究所
Keywords:	Gaussian;經驗特徵函數;經驗分布函數;穩定型分布;Cauchy;Levy;empirical distribution function;empirical characteristic function;Cauchy;stable distribution
Date:	2009-05-15
Issue Date:	2009-09-22 11:10:27 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	令X,X_1,X_2,......,X_k為一獨立且同分布的穩定型隨機變數其冪數為1/alpha 。本文中，我們以經驗分布函數估計法和經驗特徵函數估計法提出alpha的兩種估計量及其中央極限定理。當我們考慮穩定型分布分別為Gaussian,Cauchy和 Levy時，我們發現若以極限變異數之最小值為比較標準，則以經驗分布函數為基礎之估計式較佳。 Let$X,X_1,X_2,......,X_k$ be a sequence of i.i.d. stable random variables with exponent,$frac{1}{alpha }$. In this paper, we propose estimators of alpha based on empirical distribution and empirical characteristic function and derive their central limit theorems base which comparisions can be made. We find that estimator based on empirical　characteristic function is better in the sense of having smaller minimum limiting variance, when Gaussian,Cauchy and Levy are considered.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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