在本文中使用七種不同的抽樣方法估計對稱分配的位置參數，目的是為了縮減估計值的變異數。我們考慮的方法是四種逐次估計量、Trimmed Mean、修正隨機估計量和加權隨機估計量。本文利用電腦模擬的方式，比較在觀察值為標準常態分配之下這幾種估計量與簡單隨機抽樣的樣本平均數估計值的變異數大小。 / In this paper seven sampling methods are used to estimate the mean of symmetric distributions. Our goal is reduce the variance of the estimate. The methods we consider include four sequential estimators, trimmed mean, adjusted random estimator, and weighted random estimator. This paper uses the method of computer simulation to compare variance of these estimators with sample mean using simple random sampling method under standard normal distribution.

在台灣學習華語的外籍學生人數不斷增加，在今年已超過一萬五千人 。世界各國學生來台除了希望能夠在華語課程精進語言以外，更希望透過與母語人士接觸，及浸淫在中華文化下，使學習能夠更加貼近。華語中心是外籍學生對外的重要窗口，而華語中心裡的行政人員便扮演相當重要的角色。除了處理語言課程相關事務之外，也帶領學生參與課外的活動，其中包含與學生大量與密切的互動。外籍學生在目的語環境中生活，除了課堂上接觸華語，生活也與華語息息相關。截至2013年全台灣已有三十四所教育部有案登記之大學附設華語中心 ，本研究認為具有優良服務品質的華語中心才能達到外籍生就讀前的期望，外籍學生對於華語中心行政人員之滿意度影響亦其續讀意願。本研究擬針對台灣中部四所大學附設華語中心進行問卷調查。再以統計方式檢測外籍學生對華語中心行政人員的滿意度，本研究期結果能成為外籍學生在挑選學校時的參考之一，也讓大眾了解外籍學生對華語中心的看法，除此之外，也更重視華語中心行政人員之價值。

第一章: 前言介紹本文之主要內容以及所用的觀念。 第二章: 說明線性分類程序之概觀。 第三章: 討論機率預測值與個體值的關係。 第四章: 明列分對個體比率的上下限期望值。 第五章: 提出二元變數之機率預測值未知時的處理模型。 第六章結論。

在具有多變性、不確定性與訊息不完整的資訊網路時代，過去使用單一數值樣本來計算統計參數的方法，似乎已漸不符合現今多變與複雜的環境的需求。尤其在財金領域的資料採礦(data mining)研究中，利用模糊統計分析與軟計算方法，將會是一種更為接近實務需要的測度與估計工具。本研究提出模糊期望值的定義及一些相關性質，希望能配合隸屬度函數之觀念，將多元思維取代傳統二元邏輯的思考模式。並對複雜的財金問題，提出更符合人類社會行為及思考模式之實務探討。

台灣風險基礎資本額制度實施至今已將近七年，但風險係數卻從未調整，本研究主要針對股票指數與匯率之風險係數探討其是否有更新之必要，藉由1986年12月至2009年12月之資料，利用GARCH模型及EGARCH模型進行風險係數之估計，除了和風險基礎資本額制度相同，以風險值為考量外，另外加入條件尾端期望值，並比較其與風險值之差別。 實證結果發現，僅部分財務時間序列有顯著之槓桿效果，因此使用GARCH模型估計風險係數較為合適；所估計之風險係數，無論是股價指數或是匯率，其估計結果皆比現行標準高出許多。 / In Taiwan, Risk-based capital (RBC) is set up in 2003. From 2003 until now, no matter how the economical environment has changed, the risk factors have remained all the same.This research mainly focuses on the risk factors of stock index and foreign exchange and wants to know if the risk factors need to be changed. The data this research encompasses is from December 1986 to December 2009.The risk factors are estimated by GARCH model and EGARCH model, utilizing not only the VaR but also the conditional tail expectation (CTE). From the result, only a few financial time series have shown leverage effect, therefore it is indeed more appropriate to apply GARCH model in risk factors estimation. Moreover, the risk factors from the result of this research, whether it is stock index or foreign exchange rate, are significantly higher than the risk factors standard applicable in Taiwan at the present.

由於電腦革命的成功，在短暫的幾年之間，更加速了經濟的成長，而金融的投資分析，是社會經濟發展的原動力，因此研究這方向的財務數學也相對的提高了專家、學者的研究熱潮。就以股票、匯率市場來說，如果能比别人早一步掌握行情走勢，就能獲得較高的利潤。但影響股價、匯率波動的因素很多，尤其是在複雜多變及不確定性的資訊下。因此；如何進行更精確的趨勢分析與預測，是本文研究的主題。由於，傳統的期望值是二元的邏輯思考(非1即0)，比較無法符合多變與不確定的財金問題，因此本文考慮以模糊統計方法，以模糊期望值的方法來作趨勢分析與預測，期望能對複雜多變的財金體系提共一套更精確合理的投資分析方法，可以提供投資者更多的訊息，做出明確的抉擇。最後；以我國集中市場加權股票指數、台幣對美元匯率及台積電股價為例，做一實例上的詳細探討。 / Based on computer revolutionary coming off, economics grows fast in previous several years, then the investment analyze of finance is the impetus of development of society economic. Therefore, many experts and scholars are interested in the research of financial mathematics. Taking stock market and exchange market for example, if you can predict the future trend of market, you obtain more profit. However, there are many factors that act on stock prices and exchange rate. Especially, the market information is complicated and incomplete. How to go along accurate trend analysis and divination is the important point of the text research. Because traditional expectation value is dibasic logic thought (either 1 or 0), that can’t conform to the highly changeable and uncertain finance problems. For this reason, in this research we propose an integrated procedure for fuzzy expectation value modeling and forecasting through fuzzy relation equations. We apply this technique to construct a fuzzy expectation value model for Taiwan Weighted Stock Index and exchange rate and forecast future trend. We strongly believe that this model will be profound of meaning in forecasting future trend of financial market.

Artzner等學者在1999年提出風險測量值應具備同調（coherent）性質，然而，涉險值並未能完全符合。本文針對Wirch ＆ Hardy（1999）提出滿足Artzner et al.（1999）所定義同調性質之風險量化指標如條件尾端期望值（Conditional Tail Expectation；又稱尾端涉險值，Tail-VaR）以及危險比例（proportional hazards；PH）、雙重次方（dual power；DP）變形函數（distortion function）等風險衡量方法作探討，參考MGWP（1980）、Boyle ＆ Hardy（1997）、Hardy（2000）、Yang（2001）、Wilkie ＆ Waters ＆ Yang（2003）對於附保證給付之投資連結型保險契約提存準備金的方法，將其應用到保險公司所發行的附保證給付之風險量化上，同時比較其與涉險值之差異。其中之數值分析將以附最低死亡保證給付（Guarantee Minimum Death Benefit）之變額年金，以及附保證年金選擇權（Guaranteed Annuity Options）之單位連結（Unit-linked）保險商品作為範例，分別以台灣、英國兩地的投資環境為背景，檢視其附保證給付之投資型保單可能面臨的風險暴露，提供保險公司作為提存投資型商品保證給付部分之責任準備金參考。 / In this paper we introduce the properties of a coherent risk measure（Artzner et al（1999））. The risk measure of Value at Risk that does not adhere to the consistency requirements is discussed. We consider the coherent risk measures of conditional tail expectation（also known as Tail-VaR）, proportional hazards and dual power distortion functions outlined by Wirch and Hardy（1999）. MGWP（1980），Boyle and Hardy（1997），Hardy（2000），Yang（2001），Wilkie, Waters and Yang（2003）use VaR and the latter two papers also apply conditional tail expectation to reserve for investment-linked contracts with guaranteed risk. Instead, we apply the coherent measures to reserve two different types of guarantee：guarantee minimum death benefit and guaranteed annuity options attached to variable annuity contracts and unit-linked contracts separately. In addition, the comparison of the numerical results for VaR risk measure and coherent risk measure are analyzed.

近年來由於醫療技術之進步再加上物價不斷調漲的影響，使得老年人在退休時需要更多的財富來因應及保障基本的生活支出，故退休規劃對於老年人而言是個不可不重視的議題，且年金保險的設計就是在保障老年人的經濟生活不虞匱乏的一種方式，故本文主要採取之策略為自我資產配置一段期間後再將所有的財富轉換成年金。本篇使用靜態及半動態式的資產配置並配合退休者的風險容忍程度，找出退休者在退休後最適的投資策略及最適購買年金保險的時點。本文中，風險控制之設定乃是採用尾端條件期望值(CTE)的概念，且會設定兩種不同的目標函數，一個為有考慮遺產動機之函數，另一個則無考慮，最後再找出各個之結果。最後，本文也有考慮兩個比較符合實務的例子。第一，當保險公司銷售年金商品時加入附加費用率，對於退休者最適年金化年齡之影響。第二，實務上，一般退休者對於自我資金上的運用可能會拆成兩部分，一部分之資產用於購買年金保險，剩下另一部分為自我做資產配置，最後再比較此策略與全部自我資產配置再年金化策略之結果。

「風險決策」行為非常普遍的存在於吾人之日常生活中，而選項所帶來的風險和獎勵是吾人進行決策時的重要考量因素。風險選擇的適當與否，對於個體的生存扮演著相當重要的角色。在以往的文獻中，對於決策的行為歷程已有所關注及探討，但對於風險選擇行為的神經生理機制迄今未明。本研究藉由大白鼠於T字迷津中，選擇確定之低酬賞或高不確定性之高酬賞的行為表現，進行風險選擇行為的探討。本研究中以兩項主要實驗，探討風險選擇行為之神經行為機制。實驗1a中，確定之低酬賞端固定呈現1顆食物粒，而高不確定性之高酬賞端則同時操弄酬賞物機率(50%、25%及12.5%)以及酬賞物的量(2、4及8顆)，以系統性地檢驗期望值(0.5、1和2)於此風險選擇行為中扮演的角色。行為結果顯示當風險較低時，大白鼠會選擇高不確定性之高酬賞端；而風險較高時，則轉為選擇確定之低酬賞端。實驗1b中，系統性地施打不同劑量之安非他命，探討多巴胺系統在此風險選擇行為中之機制。實驗結果顯示施打安非他命後，大白鼠表現出相對地追求風險之行為，亦即選擇高不確定之高酬賞端之比例顯著高於控制組。實驗2中，藉由毀除大腦特定部位(依核、背外側之紋狀體、眶前額皮質、內側之前額皮質)，檢驗風險選擇行為之神經基礎。毀除後之結果顯示，僅有依核受到毀除之大白鼠表現出相對地趨避風險之選擇行為。綜合以上結果，本研究建立之風險選擇行為與多巴胺有關，而依核在此行為歷程中扮演重要的調節角色。 / Many decisions people make every day involve uncertainty where both risks and rewards associated with each option need to be considered. Behavioral performance associated to risk-based choice appears wildly over the lifespan, and the fitness of risky choice behavior plays an important role in individual survival. Despite a growing body of research has focused to investigate the neurobiology of decision making, little is known about the neurobehavioral mechanisms of risky choice behavior. Based on a pilot work, this study used a T-maze to study decision under a probability-based risk in the rat. The subject was assessed on making choice to obtain either a large reward associated with risk of non-reward “empty” or a small reward ensured for every entry. Two experiments were conducted in this project to investigate neurobehavioral mechanisms of probabilistic risky choice behavior. In Experiment 1a, probabilistic risky choice behavior was systemically assessed under three expected values (0.5, 1.0, and 2.0) by manipulating the probabilities of reward presence (50%, 25%, and 12.5%) and the reward magnitude (2, 4, or 8 pellets) in the probabilistic high reward (PHR) arm. Behavioral data showed that the subject chose the probabilistic high reward in a lower risk condition but would shift to the choice of certain low reward (CLR) as the risk is increased. In Experiment 1b, the dose effects of amphetamine on this probabilistic risky choice task was tested to verify whether the dopaminergic mechanism was involved. Amphetamine, presumably activating brain dopamine systems, produced a relatively risk-seeking effect on the present behavioral task. In Experiment 2, the excitoneurotoxic lesion was conducted in the nucleus accumbens, the dorsolateral striatum, the orbitofrontal cortex, and the medial prefrontal cortex to examine the neural substrates for this probabilistic risky choice behavior. The results showed that the lesion of the nucleus accumbens significantly produced a relatively risk-averse effect on the present behavioral task, as compared to the lesions made on the other three brain areas. In conclusion, the probabilistic risky choice behavior established in the present study is dopamine dependent. And, the nucleus accumbens plays a major role of mediating this behavioral processing.

在許多實際情形下，傳統的統計檢定方法是不足以應付的。故本論文提出模糊檢定方法，我們定義出模糊樣本期望值與模糊樣本變異數的計算方法，再針對不同的模糊資料，分別提出不同的檢定方法，去解決最實際需要解決的問題，其中包括推廣古典的統計檢定方法與自創的檢定方法。 關鍵字：隸屬度函數，模糊樣本取樣，模糊樣本期望值，模糊樣本變異數，人性思考，t檢定，F檢定，模糊常態分配。 / In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this paper, we present a class of fuzzy statistical decision process in which testing hypothesis can be naturally reformulated in terms of interval-valued statistics. We provide the definitions of fuzzy mean, fuzzy distance as well as investigation of their related properties. We also give some empirical examples to illustrate the techniques and to analyze fuzzy data. Empirical studies show that fuzzy hypothesis testing with soft computing for interval data are more realistic and reasonable in the social science research. Finally certain comments are suggested for the further studies. We hope that this reformation will make the corresponding fuzzy techniques more acceptable to researchers whose only experience is in using traditional statistical methods. Key words: Membership function, fuzzy sampling survey, fuzzy mean, human thought, t-test, F-test, normally distributed.