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121	簡單順序假設波松母數較強檢定力檢定研究 -兩兩母均數差 / More Powerful Tests for Simple Order Hypotheses in Poisson Distributions -The differences of the parameters 孫煜凱, Sun, Yu-Kai Unknown Date (has links) 波松分配（Poisson Distribution）常用在單位時間或是區間內，計算對有興趣之某隨機事件次數（或是已知事件之頻率），例如：速食餐廳的單位時間來客數，又或是每段期間內，某天然災害的發生次數，可以表示為某一特定事件X服從波松分配，若lambda為單位事件發生次數或是平均次數，我們稱lambda為此波松分配之母數，記作Poisson(lambda)，其中lambda屬於實數。今天我們若想要探討由兩個服從不同波松分配抽取的隨機變數，如下列所述：令X={(X1,X2)}為一集合，其中Xi為X(i,1),X(i,2),...,X(i,ni)~Poisson(lambda(i)),i=1,2。欲探討兩波松分配之均數是否相同或相差小於某個常數d時，考慮以下檢定:H0:lambda2-lambda1<=d與H0:lambda2-lambda1>d，對於此問題可以使用的檢定方法有Przyborwski和Wilenski(1940)提出的條件檢定（Conditional test,C-test）或K.Krishnamoorthy與Jessica Thomson(2002)提出的精確性檢定（Exact test,E-test），其中的精確性檢定為一個非條件檢定（Unconditional Test）；K.Krishnamoorthy與Jessica Thomson比較條件檢定與精確性檢定的p-value皆小於顯著水準(apha)，而精確性檢定的檢定力不亞於條件檢定，因此精確性檢定比條件檢定更適合上面所述之假設問題。 Roger L.Berger（1996）提出一個以信賴區間的p-value所建立的較強力檢定，而目前只用於檢定兩二項分配（Binomial Distribution）的機率參數p是否相同為例，然而Berger在文中提到，較強力檢定比非條件檢定有更好的檢定力，而且要求的計算時間較少，可以提升檢定的效率。本篇論文我們希望在固定apha與d時檢定的問題，建立一個兩波松分配均數顯著水準為apha的較強力檢定。利用Roger L.Berger與Dennis D.Boos(1994)提出以信賴區間的p-value方法，建立波松分配兩兩母均數差的較強力檢定；研究發現此較強力檢定與精確性檢定的p-value皆小於apha，然而我們的檢定的檢定力皆不亞於精確性檢定所計算得出的檢定力，然而其apha及虛無假設皆需要善加考慮以本篇研究來看，當檢定為單尾檢定時，若apha<0.01，我們的較強力檢定沒有辦法找到比精確性檢定更好地拒絕域，換言之，此時較強力檢定與精確性檢定的檢定力將會相等。 / Poisson Distribution is used to calculate the probability of a certain phenomenon which attracted by researcher. If we want to test two random variable in an experiment .Therefore ,let X={(X1,X2)} be independent samples ,respectively ,from Poisson distribution ,also X(i,1),X(i,2),...,X(i,ni)~Poisson(lambda(i)),i=1,2. The problem of interest here is to test: H0:lambda2-lambda1<=d and H0:lambda2-lambda1>d, where 0<apha<1/2 ,and let Y1 equals sum of X1 and Y2 equals sum of X2, where apha ,lambda,d be fixed. In this problem of hypothesis testing about two Poisson means is addressed by the conditional test.However ,the exact method of testing based on the test statistic considered in K.Krishnamoorthy,Jessica Thomson(2002) also commonly used. Roger L.Berger ,Dennis D.Boos(1994) give a new way to calculate p-value,which replace the old method ,called it a valid p-value .In 1996, Roger L.Berger used the new way to propose a new test for two parameter of binomial distribution which is more powerful than exact test. In the other hand, Roger L.Berger also explain the unconditional test is more suitable than the conditional test. In this paper,we propose a new method for two parameter of Poisson distribution which revise from Roger L.Berger’s method. The result we obtain that our new test is really get a much bigger rejection region.We found when the fixed increasing ,the set of more powerful test increasing, and when the fixed power increasing ,the required sample size decreasing. 波松分配條件檢定精確性檢定較強力檢定信賴區間蒙地卡羅法 Poisson distribution Conditional test Exact test More powerful test Confidence set Monte carlo method
122	時間電價系統的最佳契約容量 / Optimal contract capacities for Time-of-Use electricity pricing systems 王家琪, Wang, Jia Qi Unknown Date (has links) 隨著各行各業的飛速發展、科技的不斷進步，一般的公司行號、工廠及現代化的建築對於電力需求大大增加。但是在有限的電力資源下，有時候一到用電高峰時期，很難滿足各行各業的用電需求，因此難免會出現很多地方在用電高峰期跳電的情況。電力公司為了更加有效的分配電力，提出所謂時間電價的概念，和用戶實現簽訂各自的契約容量，將這個契約容量作為每個月分配給各個用戶的最大電量標準。對於用戶來說，若選擇相對較低的契約容量，其所需要負擔的基本電費會較低。然而，當用電量超過契約容量時，用戶可能需要支付非常高額的罰款；若選擇相對較高的契約容量，雖然其支付高額罰款的機率會降低很多，但是所需要負擔的基本電費會增多。因此，對於電力公司和用戶而言，使用時間電價系統，來選擇一個適當的且最佳化的契約容量，已然成為一個非常重要的課題。本文介紹如何用分形布朗運動的模型，來描述用戶用電量趨勢，同時介紹了如何估計分形布朗運動模型中的各個參數。本文也介紹如何建立每月總電費期望值的估計方程式，並利用估計出來的用電量分形布朗運動模型來搜尋最佳化的契約容量。最後，本文以美國密西根州的安娜堡的居民住宅大樓用電量為數據資料作為研究的實例，進一步的提出並論證了選擇最佳化契約容量的方法。 / Over the last few decades, the advances in technology and industry have significantly increased the need of electric power, while the power resource is usually limited. In order to best control the power usage, a so-called Time-of-Use (TOU) pricing system is recently developed so that different rates over different seasons and/or weekly/daily peak periods are charged (this is different from the traditional pricing system with flat rate contracts). An important feature of the TOU system is that the consumers have to pre-select the power contract capacities (i.e. the maximum power demands claimed by consumers over different pricing periods) so that the electricity tariff can be calculated accordingly. This means that risk is transferred from the retailer side to the consumer side -- one has to pay more if a larger contract capacity is selected but can potentially mitigate the penalty charge placed when the maximum demand exceeds the contract level. In this thesis, a general stochastic modeling framework for consumer's power demand based on which the contract capacities of a Time-of-Use pricing system can be best selected so as to minimize the mean electricity price. Due to the observed nature of self-similarity and time dependence, the power demand over a homogeneous peak period is modeled as a constant mean with the noise described by a scaled fractional Brownian motion. However, the underlying optimization problem involves an intricate mathematical formulation, thus requiring techniques such as Monte Carlo simulation and numerical search so as to estimate the solution. Finally, a real data set from Ann Arbor, Michigan along with two pricing systems are used to illustrate our proposed method. 時間電價系統最佳化契約容量分形布朗運動赫斯特指數離散變異法蒙地卡羅模擬 Time-of-Use pricing system Optimum contract capacity Fraction Brownian Motion Hurst Parameter Discrete Variation Method Monte Carlo Simulation
123	複迴歸係數排列檢定方法探討 / Methods for testing significance of partial regression coefficients in regression model 闕靖元, Chueh, Ching Yuan Unknown Date (has links) 在傳統的迴歸模型架構下，統計推論的進行需要假設誤差項之間相互獨立，且來自於常態分配。當理論模型假設條件無法達成的時候，排列檢定（permutation tests）這種無母數的統計方法通常會是可行的替代方法。在以往的文獻中，應用於複迴歸模型（multiple regression）之係數排列檢定方法主要以樞紐統計量（pivotal quantity）作為檢定統計量，進而探討不同排列檢定方式的差異。本文除了採用t統計量這一個樞紐統計量作為檢定統計量的排列檢定方式外，亦納入以非樞紐統計量的迴歸係數估計量b22所建構而成的排列檢定方式，藉由蒙地卡羅模擬方法，比較以此兩類檢定方式之型一誤差（type I error）機率以及檢定力（power），並觀察其可行性以及適用時機。模擬結果顯示，在解釋變數間不相關且誤差分配較不偏斜的情形下，Freedman and Lane (1983)、Levin and Robbins (1983)、Kennedy (1995)之排列方法在樣本數大時適用b2統計量，且其檢定力較使用t2統計量高，但差異程度不大；若解釋變數間呈現高度相關，則不論誤差的偏斜狀態，Freedman and Lane (1983)、Kennedy (1995) 之排列方法於樣本數大時適用b2統計量，其檢定力結果也較使用t2統計量高，而且兩者的差異程度比起解釋變數間不相關時更加明顯。整體而言，使用t2統計量適用的場合較廣；相反的，使用b2的模擬結果則常需視樣本數大小以及解釋變數間相關性而定。 / In traditional linear models, error term are usually assumed to be independently, identically, normally distributed with mean zero and a constant variance. When the assumptions cannot meet, permutation tests can be an alternative method. Several permutation tests have been proposed to test the significance of a partial regression coefficient in a multiple regression model. t=b⁄(se(b)), an asymptotically pivotal quantity, is usually preferred and suggested as the test statistic. In this study, we take not only t statistics, but also the estimates of the partial regression coefficient as our test statistics. Their performance are compared in terms of the probability of committing a type I error and the power through the use of Monte Carlo simulation method. Situations where estimates of the partial regression coefficients may outperform t statistics are discussed. 排列檢定複迴歸模型樞紐統計量蒙地卡羅模擬型一誤差檢定力 Permutation test Multiple regression model Pivotal quantity Monte Carlo simulation Type I error Power
124	競爭風險下長期存活資料之貝氏分析 / Bayesian analysis for long-term survival data 蔡佳蓉 Unknown Date (has links) 當造成失敗的原因不只一種時，若各對象同一時間最多只經歷一種失敗原因，則這些失敗原因稱為競爭風險。然而，有些個體不會失敗或者經過治療之後已痊癒，我們稱這部分的群體為治癒群。本文考慮同時處理競爭風險及治癒率的混合模式，即競爭風險的治癒率模式，亦將解釋變數結合到治癒率、競爭風險的條件失敗機率，或未治癒下競爭風險的條件存活函數中，並以建立在完整資料上之擴充的概似函數為貝氏分析的架構。對於右設限對象則以插補方式決定是否會治癒或會因何種風險而失敗，並推導各參數的完全條件後驗分配及其性質。由於邊際後驗分配的數學形式無法明確呈現，再加上需對右設限者判斷其狀態，所以採用屬於馬可夫鏈蒙地卡羅法的Gibbs抽樣法及適應性拒絕抽樣法(adaptive rejection sampling) ，執行參數之模擬抽樣及設算右設限者之治癒或失敗狀態。實證部分，我們分析Klein and Moeschberger (1997)書中骨髓移植後的血癌病患的資料，並用不同模式之下的參數模擬值計算各對象之條件預測指標(CPO)，換算成各模式的對數擬邊際概似函數值(LPML)，比較不同模式的優劣。 / In case that there are more than one possible failure types, if each subject experiences at most one failure type at one time, then these failure types are called competing risks. Moreover, some subjects have been cured or are immune so they never fail, then they are called the cured ones. This dissertation discusses several mixture models containing competing risks and cure rate. Furthermore, covariates are associated with cure rate, conditional failure rate of each risk, or conditional survival function of each risk, and we propose the Bayesian procedure based on the augmented likelihood function of complete data. For right censored subjects, we make use of imputation to determine whether they were cured or failed by which risk and derive full conditional posterior distributions. Since all marginal posterior distributions don’t have closed forms and right censored subjects need to be identified their statuses, we take Gibbs sampling and adaptive rejection sampling of Markov chain Monte Carlo method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the bone marrow transplant data from the book written by Klein and Moeschberger (1997). To do model selection, we compute the conditional predictive ordinate(CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudo marginal likelihood (LMPL) of each model. 治癒率模式競爭風險混合模式擴充的概似函數馬可夫鏈蒙地卡羅方法(MCMC) 完全條件後驗分配 Gibbs 抽樣法條件預測指標(CPO) 對數擬邊際概似函數值(LPML) cure rate models competing risks mixture models augmented likelihood functions Markov Chain Monte Carlo method(MCMC) full conditional posterior distributions Gibbs samplings conditional predictive ordinate(CPO) log of pseudo marginal likelihood(LPML)
125	含存活分率之貝氏迴歸模式李涵君 Unknown Date (has links) 當母體中有部份對象因被治癒或免疫而不會失敗時，需考慮這群對象所佔的比率，即存活分率。本文主要在探討如何以貝氏方法對含存活分率之治癒率模式進行分析，並特別針對兩種含存活分率的迴歸模式，分別是Weibull迴歸模式以及對數邏輯斯迴歸模式，導出概似函數與各參數之完全條件後驗分配及其性質。由於聯合後驗分配相當複雜，各參數之邊際後驗分配之解析形式很難表達出。所以，我們採用了馬可夫鏈蒙地卡羅方法（MCMC）中的Gibbs抽樣法及Metropolis法，模擬產生參數值，以進行貝氏分析。實證部份，我們分析了黑色素皮膚癌的資料，這是由美國Eastern Cooperative Oncology Group所進行的第三階段臨床試驗研究。有關模式選取的部份，我們先分別求出各對象在每個模式之下的條件預測指標（CPO），再據以算出各模式的對數擬邊際概似函數值（LPML），以比較各模式之適合性。 / When we face the problem that part of subjects have been cured or are immune so they never fail, we need to consider the fraction of this group among the whole population, which is the so called survival fraction. This article discuss that how to analyze cure rate models containing survival fraction based on Bayesian method. Two cure rate models containing survival fraction are focused; one is based on the Weibull regression model and the other is based on the log-logistic regression model. Then, we derive likelihood functions and full conditional posterior distributions under these two models. Since joint posterior distributions are both complicated, and marginal posterior distributions don’t have closed form, we take Gibbs sampling and Metropolis sampling of Markov Monte Carlo chain method to simulate parameter values. We illustrate how to conduct Bayesian analysis by using the data from a melanoma clinical trial in the third stage conducted by Eastern Cooperative Oncology Group. To do model selection, we compute the conditional predictive ordinate (CPO) for every subject under each model, then the goodness is determined by the comparing the value of log of pseudomarginal likelihood (LPML) of each model. 存活分率貝氏治癒率模式 Weibull迴歸模式對數邏輯斯迴歸模式完全條件後驗分配馬可夫鏈蒙地卡羅方法 Gibbs抽樣法條件預測指標對數擬邊際概似函數值 surviving fraction Bayesian cure rate models Weibull regression model log-logistic regression model full conditional posterior distributions Markov chain Monte Carlo method (MCMC) Gibbs sampling conditional predictive ordinate (CPO) log of pseudomarginal likelihood (LPML)
126	市場風險值管理之應用分析以某金融控股公司為例 / The analysis of Market Risk VaR management ：the case of financial holding company 周士偉, Chou, Jacky Unknown Date (has links) 2008年次貸風暴橫掃全球金融市場，Basel II制度歷經多年的實施，卻無法有效防阻金融風暴的發生。觀察2008已採用內部模型法之主要國際金融機構之年報，亦發現採用蒙地卡羅模擬法之代表銀行『德意志銀行』於該年度竟發生了35次穿透，市場風險管理到底出了什麼問題？這是被極度關心的現象，產官學界也對此現象提出了許多議題。2012年的現在，次貸的風暴尚未遠去，新的歐債危機也正在蔓延，若金融風暴再次來臨，市場風險管理是否能克服次貸風暴後所凸顯的缺失，市場風險管理的價值除被動管理外，是否還可以進階到主動預警，以作為經營決策的重要參考資訊？這些都是國內金融機構需積極面對的急迫的市場風險管理議題。個案金控的市場風險管理機制致力於解決次貸以來所凸顯的市場風險管理議題、提升市場風險衡量的精準度、擴大市場風險管理之應用範圍，並將市場風險管理的價值由被動管理角色進階到主動預警角色，以期作為經營決策的重要參考。經過多年的淬煉，其發展理念與經驗應具相當參考價值，故本論文以個案金融控股公司(以下簡稱個案金控)之實務經驗進行個案研究，除分析個案金控市場風險管理機制的基礎架構外，也將研究重心放在個案金控如何在此基礎架構下，開發多種進階市場風險量化管理功能。本論文除研究個案金控如何完善市場風險值量化機制外，也對各量化功能的實施結果進行分析，以期研究成果可更客觀的作為其他金融控股公司未來發展進階市場風險衡量機制之參考。市場風險風險值經濟價值信託基金操作風險風險因子一般風險值壓力風險值條件風險值增額風險值邊際風險值變異數-共變異數法歷史模擬法蒙地卡羅模擬法隱含波動度厚尾順景氣循環標準法內部模型法市場流動性風險外生性市場流動性風險內生性市場流動性風險流動性調整後風險值壓力測試回溯測試 Market Risk Value at Risk Economic Value Active Management VaR Tracking Error Risk Factor Common VaR Stressed VaR Conditional VaR Incremental VaR Marginal VaR Variance-Covariance Approach Historical Simulation Approach Monte Carlo Simulation Approach Fat Tail Time-Varying Volatility pro-cyclical Standardized Approach Internal Models Approach Implied Volatility Generalized Error Distribution Bernoulli trial test Likelihood ratio test Unconditional Coverage Test Conditional Coverage Test Backward Looking Model Forward Looking Model Forecasting VaR Pearson Correlation Cholesky decomposition Kendall Correlation Copula method Future Volatility Disconnection Market Liquidity Risk Exogenous Market Liquidity Risk Endogenous Market Liquidity Risk Liquidity-adjusted VaR Stress Test Backtesting Net Interest Income Re-pricing Model Maturity Model Duration Model

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