分布函數之反函數之核估計的模擬研究; A Simulation Study for Kernel Estimator of Inverse Distribution Function

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7948

Title:	分布函數之反函數之核估計的模擬研究;A Simulation Study for Kernel Estimator of Inverse Distribution Function
Authors:	李世懿;Shih-yi Li
Contributors:	數學研究所
Keywords:	分布函數之反函數;核估計;inverse distribution function;kernel estimator
Date:	2008-05-24
Issue Date:	2009-09-22 11:09:53 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	分布函數為機率上重要的分析工具，其重要性不亞於機率密度函數及特徵函數。在統計上分布函數也有很多應用，令$F$表一分布函數，則$F^{-1}$可用於隨機變數之模擬及穩定型分布(stable distribution)之冪數(exponent)的估計。通常分布函數是未知的，必需用樣本估計。分布函數未知時，常用之分布函數的估計式為經驗分布(empirical distribution function)。本文之目的為研究$F^{-1}$的估計，但上述經驗分布卻因其反函數不存在，故不能直接運用。本文提出$F^{-1}(y)$之核估計式$widehat{F}^{-1}(y)$，因此式之機率性質非常複雜，故本文將以電腦模擬方式研究$widehat{F}^{-1}(y)$之漸近一致性(asymptotic consistency)及漸近常態性(asymptotic normality)。 The inverse function of a distribution function has many applications in statistics. In practice, the inverse function is unknown and has to be estimated. The purpose of this paper is to discuss a kernel estimator $widehat{F}^{-1}(y)$ of the inverse function $F^{-1}(y)$ of a distribution function $F(x)$. Since the theoretical property of $widehat{F}^{-1}(y)$ is extremely complicated, we will investigate the asymptotic consistency and asymptotic normality of $widehat{F}^{-1}(y)$ via computer simulations.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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