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研究生:詹建峰
研究生(外文):ZHAN, JIAN-FENG
論文名稱:NormalInverseGaussian分配其檢定之探討
論文名稱(外文):TESTING FOR SYMMETRY IN NORMAL INVERSE GAUSSIAN DISTRIBUTION
指導教授:劉惠美劉惠美引用關係洪明欽洪明欽引用關係
指導教授(外文):LIU, HUI-MEIHONG , MING-QIN
學位類別:碩士
校院名稱:國立臺北大學
系所名稱:統計學系
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:39
中文關鍵詞:Normal Inverse Gaussian分配Inverse Gaussian分配厚尾分配EM演算法Wald檢定最大概似比檢定漸近分配
外文關鍵詞:Normal Inverse Gaussian DistributionsInverse Gaussian DistributionsNormal Variance-mean Mixtur- es With An Inverse Gaussian Mixing DistributionLikelihood Ratio TestsWald TestAsymptotic DistributionEM Algorithm .
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Normal Inverse Gaussian分配模型在財務上的運用,近來日益受到重視。Normal Inverse Gaussian分配是一個由Inverse Gaussian分配和Normal分配混合而成的分配,由於該分配非常適合用來描繪財務上一些具有厚尾分配或顯著偏斜的隨機現象,是故,得以漸漸取代了先前普遍使用的Student’s T 分配而逐漸受到青睞。
而Normal Inverse Gaussian分配的形成過程,是在給定服Inverse Gaussian 分配的z之下,假設x的條件分配為期望值是mu+beta*z,變異數為z的常態分配,其中若從財務的觀點來看x的期望值,該假設認為波動是有可能對期望報酬造成影響的,也就是認為當波動越大時,期望報酬理應隨之越大才較為合理,然而其影響與否,端賴參數bets是否等於0而定。
本研究主要是對Normal Inverse Gaussian分配的參數beta是否等於0,作一些統計檢定的探討。然而,因Normal Inverse Gaussian分配是一個頗為複雜的分配,在檢定beta時,本文使用了漸進理論中最大概似比檢定其漸近分配的性質,並和同是大樣本近似檢定的Wald檢定作比較。

This thesis aims primarily to test the symmetry in Normal Inverse Gaussian distributions which act as Normal variance-mean mixtures with an Inverse Gaussian mixing distribution.
Due to the complicated structure of normal inverse gaussian distribution, two approximate large-sample tests are to be applied. One of the two methods is by way of asymptotic distribution of likelihood ratio tests, another method of constructing a large-sample test statistic is based on an estimator that has an asymptotic normal distribution. An EM type algorithm is provided for the Maximum Likelihood estimation of the Normal Inverse Gaussian distribution in the two methods. Finally, according to the simulation results some conclusions are given.

摘要
壹、緒論………………………………………………………………1
貳、文獻回顧……………….………………………………………4
一、Inverse Gaussian分配………………………………………4
二、Normal Inverse Gaussian分配………………………………4
三、Normal Inverse Gaussian分配動差估計……………………7
四、利用EM演算法求NIG分配之最大概似估計值………………8
參、研究方法………………………………………………………15
一、最大概似比檢定的漸進分配性質……………………………15
二、Wald檢定………………………………………………………21
肆、模擬比較…………………………………………………………23
伍、結論與建議………………………………………………………31
附錄一…………………………………………………………………32
附錄二…………………………………………………………………35
參考文獻………………………………………………………………38

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