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 研究機率分佈的性質一直以來都是統計和應用機率領域的主要課題。本論文主要經由下列兩個主題來探討分佈函數：(i) 基於記錄值和順序統計量的分佈刻劃 (ii) 關於偏斜t分佈的性質。在刻劃文獻中，有很多結果隱含關於記錄值和順序統計量的性質。雖然在基於記錄值和順序統計量的刻劃中，已經有許多大家熟悉的結果，但是發掘新的刻劃結果仍相當吸引人的。本論文的第一部分，將給出在給定最大順序統計量之下，任何一個記錄值的條件分佈。接著探討基於記錄值和最大順序統計量的分佈刻劃。此外，也會在順序統計量的點過程當中，藉由到達時刻或現在壽命的條件動差之間的某些關係，來刻畫點過程的期望函數。這些結果可應用在順序統計量中對均勻分佈的刻劃，和記錄值中對指數分佈的刻劃。 Azzalini (1985, 1986)提出的偏斜常態分佈，不僅涵蓋常態分佈，且具有一些與常態分佈相同的性質。此類分佈有助於穩健性的研究和偏斜性的建模。此後，便有許\多人投入基於對稱分佈的偏斜分佈之研究。本論文的第二部分，將定義和研究所謂的廣義偏斜t分佈，並給出一些例子。這些例子是由兩個獨立的偏斜對稱隨機變數相除所產生的。最後我們也會對偏斜對稱分佈的性質作一些探討。
 The study of properties of probability distributions has always been a persistent theme of statistics and of applied probability. This thesis deals with an investigation of distribution functions under the following two topics: (i) characterization of distributions based on record values and order statistics, (ii) properties of the skew-t distribution.Within the extensive characterization literature there are several results involving properties of record values and order statistics. Although there have been many well known results already developed, it is still of great interest to find new characterization of distributions based on record values and order statistics. In the first part, we provide the conditional distribution of any record value given the maximum order statistics and study characterizations of distributions based on record values and the maximum order statistics. We also give some characterizations of the mean value function within the class of order statistics point processes, by using certain relations between the conditional moments of the jump times or current lives. These results can be applied to characterize the uniform distribution using the sequence of order statistics, and the exponential distribution using the sequence of record values, respectively.Azzalini (1985, 1986) introduced the skew-normal distribution which includes the normal distribution and has some properties like the normal and yet is skew. This class of distributions is useful in studying robustness and for modeling skewness. Since then, skew-symmetric distributions have been proposed by many authors. In the second part, the so-called generalized skew-t distribution is defined and studied. Examples of distributions in this class, generated by the ratio of two independent skew-symmetric distributions, are given. We also investigate properties of the skew-symmetric distribution.
 1 Introduction 12 Characterizations based on record values and order statistics 72.1 Introduction 72.2 The conditional distribution of record values given Xn:n 92.3 Characterizations based on conditional expectations of record values given Xn:n 122.4 Further characterizations based on record values and Xn:n 193 Characterizations of the order statistics point process by the relations between its conditional moments 253.1 Introduction 253.2 Characterizations by using conditional moments of jump times of the process 283.3 Characterizations based on relationship of conditional moments of jump time and current life 353.4 Some characterizations related to Abu-Youssef (2003) 374 A study of generalized skew-t distribution 414.1 Introduction 414.2 Preliminaries 424.3 Generalized skew-t distribution 444.4 Skew-symmetric distribution 544.5 Appendix 57References 61
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 1 藉著設限樣本探討Makeham 分配的特徵性及參數加權估計 2 對稱及偏斜分佈之一些探討 3 一些關於離散記錄值之分佈刻劃 4 關於某些條件期望值的刻劃 5 偏斜對稱模型的研究 6 機率分佈之條件期望值刻劃 7 關於順序統計量之條件期望值的刻劃 8 非齊性波松過程和記錄值之探討

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 1 偏斜對稱模型的研究 2 對稱及偏斜分佈之一些探討 3 多變量偏斜分佈對於不完整資料之研究 4 關於Gamma分佈及相關問題之研究 5 財務衍生性商品定價與避險的動態半參數法 6 區間設限資料下應用多重插補法之無母數檢定 7 混合的偏斜常態分布其及應用 8 偏斜常態分佈參數估計的探討及具標準化偏斜常態誤差下母體平均值之漸近信賴區間的建構與應用 9 實數上有關對稱性概念的探討 10 二維常態分佈相關係數的較佳檢定及在偏斜常態分佈架構下相關檢定的穩健性分析 11 算子代數上的線性保正交性映射 12 混合實驗在對數對比模型之最適設計 13 偽發現率之評註 14 在偏斜常態模型下常態平均值之信賴區間的穩健性探討及偏斜參數之信賴區間與具高檢定力之不偏檢定的建構 15 生理特徵在醫療診斷問題上的應用-以血氧濃度及指紋為例

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