本文主要是研究統計理論中的聯立信賴區間估計法，針對雙特徵數的指數母體，研究 位置特徵數的差異狀況。也就是要找出位置特徵數的所有複合比，所有對比的聯立信 賴區間。全文共分四章。第一章緒論，說明研究動機、目的及方法。第二章指數分布 的順序統計式，由於本文所使用的估計方法會使用到順序統計式，所以在本章中特別 研究順序統計式的某些線性組合，找出某些特殊的性質；並且將Tanis （１９６３） 提出的理論擴展至第二型設限數據。第三章位置特徵數的聯立信賴區間，藉由第二章 中導出的定理以Tukey 法及Holder不等式法找出聯立信賴區間，並且比較這些方法的 優劣。第四章結論及建議。全文共一冊，約兩萬字。

Die Kapitel 1 bis 6 im ersten Teil dieses Skriptes beruhen auf einer Vorlesung Ökonometrie I, die zuletzt im WS 2001/02 gehalten wurde, die Kapitel 7 bis 16 beruhen auf einer Vorlesung Ökonometrie II, die zuletzt im SS 2006 gehalten wurde. Das achte Kapitel enthält eine komprimierte Zusammenfassung der Ergebnisse aus dem Teil Ökonometrie I.

Approved for public release; distribution in unlimited. / Budget limitations have reduced the number of military components available for testing, and time constraints have reduced the amount of time available for actual testing resulting in many items still operating at the end of test cycles. These two factors produce small test populations (small sample size) with "heavily" censored data. The assumption of "normal approximation" for estimates based on these small sample sizes reduces the accuracy of confidence bounds of the probability plots and the associated quantities. This creates a problem in acquisition analysis because the confidence in the probability estimates influences the number of spare parts required to support a mission or deployment or determines the length of warranty ensuring proper operation of systems. This thesis develops a method that simulates small samples with censored data and examines the error of the Fisher-Matrix (FM) and the Likelihood Ratio Bounds (LRB) confidence methods of two test populations (size 10 and 20) with three, five, seven and nine observed failures for the Weibull distribution. This thesis includes a Monte Carlo simulation code written in S-Plus that can be modified by the user to meet their particular needs for any sampling and censoring scheme. To illustrate the approach, the thesis includes a catalog of corrected confidence bounds for the Weibull distribution, which can be used by acquisition analysts to adjust their confidence bounds and obtain a more accurate representation for warranty and reliability work. / Civilian, Department of the Air Force

[pt] A apreciação ou crescimento de reservas de óleo e gás é importante para uma empresa petrolífera, pois ela indica quanto uma reserva provada crescerá desde o início da produção até um determinado ano. Cada campo apresenta uma apreciação própria que depende de diversos fatores que fazem com que as reservas que antes eram classificadas como prováveis e possíveis sejam reclassificadas agora como provadas. Esta dissertação propõe determinar a apreciação de reservas para óleo e gás com base em séries históricas de campos com características semelhantes, calculando a apreciação média e a elas associando as incertezas da previsão por meio de intervalo de confiança para cada ano após o início da produção, e assim, determinando curvas delimitadoras do intervalo. Dos modelos estudados que satisfazem à condição de monotonicidade não-crescente (a taxa de apreciação anual diminui com o tempo), têm-se o logarítmico e o hiperbólico, sendo que o logarítmico foi o que teve melhor ajuste aos dados observados. Entretanto não se deve descartar o modelo hiperbólico, pois ele tem um apelo teórico e pode ter melhor ajuste do que o modelo logarítmico dependendo dos dados. Esse estudo é de caráter teórico, pois não foi possível obter dados reais de reservas. / [en] Oil and gas reserve appreciation, or growth, is a phenomenon important to petroleum exploratory and producing companies. If well understood, the companies will improve their reserves projection into the future. Each field presents a particular appreciation that depends on various factors that move resources from an initial classification into proved reserve-classification. This thesis proposes a methodology for determining oil and gas reserves appreciation based on historical time series data from similar fields, calculating year to year average appreciation, and associating to each average a confidence interval. Two models were selected for adjustment (logarithmic and hyperbolic) both presenting monotonic non- increasing year to year growth. The logarithmic model presented better adjustment to a limited data-set but hyperbolic should not be discarded both because it has desirable features and may produce better future projections. The difficulties in obtaining adequate real historical data, and other kinds of information on reserves time series impeded further statistical analysis.

The problem of constructing a confidence interval for the noncentrality parameter of a noncentral t-distribution based upon one observation from the distribution is an interesting problem with important applications. A general theoretical approach to the problem is provided by the specification and inversion of acceptance sets for each possible value of the noncentrality parameter. The standard method is based upon the arbitrary assignment of equal tail probabilities to the acceptance set, while the choices of the shortest possible acceptance sets and UMP unbiased acceptance sets provide even worse confidence intervals, which means that since the standard confidence intervals are uniformly shorter than those of UMPU method, the standard method are "biased". However, with the correct choice of acceptance sets it is possible to provide an improvement in terms of confidence interval length over the confidence intervals provided by the standard method for all values of observation. The problem of testing the equality of the noncentrality parameters of two noncentral t-distributions is considered, which naturally arises from the comparison of two signal-to-noise ratios for simple linear regression models. A test procedure is derived that is guaranteed to maintain type I error while having only minimal amounts of conservativeness, and comparisons are made with several other approaches to this problem based on variance stabilizing transformations. In summary, these simulations confirm that the new procedure has type I error probabilities that are guaranteed not to exceed the nominal level, and they demonstrate that the new procedure has size and power levels that compare well with the procedures based on variance stabilizing transformations.

The capacitance-resistance model (CRM) has been continuously improved and tested on both synthetic and real fields. For a large waterflood, with hundreds of injectors and producers present in a reservoir, tens of thousands of model parameters (gains, time constants, and productivity indices) in a field must be determined to completely define the CRM. In this case obtaining a unique solution in history-matching large reservoirs by nonlinear regression is difficult. Moreover, this approach is more likely to produce parameters that are statistically insignificant. The nonlinear nature of the CRM also makes it difficult to quantify the uncertainty in model parameters. The analytical solutions of the two linear reservoir models, the linearly transformed CRM whose control volume is the drainage volume around each producer (ltCRMP) and integrated capacitance-resistance model (ICRM), are developed in this work. Both models are derived from the governing differential equation of the producer-based representation of CRM (CRMP) that represents an in-situ material balance over the effective pore volume of a producer. The proposed methods use a constrained linear multivariate regression (LMR) to provide information about preferential permeability trends and fractures in a reservoir. The two models’ capabilities are validated with simulated data in several synthetic case studies. The ltCRMP and ICRM have the following advantages over the nonlinear waterflood model (CRMP): (1) convex objective functions, (2) elimination of the use of solver when constraints are ignored, and (3) faster computation time in optimization. In both methods, a unique solution can always be obtained regardless of the number of parameters as long as the number of data points is greater than the number of unknowns (parameters). The methods of establishing the confidence limits on CRMP gains and ICRM parameters are demonstrated in this work. This research also presents a method that uses the ICRM to estimate the gains between newly introduced injectors and existing producers for a homogeneous reservoir without having to do additional simulations or regression on newly simulated data. This procedure can guide geoscientists to decide where to drill new injectors to increase future oil recovery and provide rapid solutions without having to run reservoir simulations for each scenario. / text

In the field of diagnostic test studies, the accuracy of a diagnostic test is essential in evaluating the performance of the test. The receiver operating characteristic (ROC) curve and the area under the curve (AUC) are widely used in such evaluation procedures. Meanwhile, the Youden index is also introduced into practice to measure the accuracy of the diagnostic test from another aspect. The Youden index maximizes the sum of sensitivity and specificity, assuring decent true positive and negative rates. It draws one's attention due to its merit of finding the optimal cut-off points of biomarkers. Similar to Partial ROC, a new index, called "Partial Youden index" can be defined as an extension of Youden's Index. It is more meaningful than regular Youden index since the regular one is just a special case of the Partial Youden Index. In this thesis, we focus on construction of generalized confidence intervals for the Partial Youden Index and its corresponding optimal cut-off points. Extensive simulation studies are conducted to evaluate the finite sample performances of the new intervals.

本研究主要是針對高中數學課程中「信賴區間」的這個單元，依據99 課綱中的課程規劃，設計出一套專題式的研究教材，並以筆者所任教高中的高二及高三學生作為研究對象，進行專題性的課程授課，且對其學習成果進行評量。主要研究結果如下： 一、高三學生雖已進行過「信賴區間」及其先備知識之授課，但前測的成績並不理想。 二、高二與高三學生經由筆者授課教學後，其後測成績均較前測成績有非常明顯之進步，不過高二與高三學生的後測成績並無顯著差異。 三、高二自然組與高二社會組學生經由筆者授課教學後，其學習成效亦無顯著差異，但社會組學生學習上普遍較為認真，後測成績稍高於自然組。 四、高三自然組與高三社會組學生經由筆者授課教學後，其後測成績具顯著差異，而進步成績的學習成效亦具有顯著差異，自然組優於社會組。 五、依高中數學學習成就分成高分群、中分群與低分群三群，雖然在前測與後測成績表現上顯著不同，但進步的成績則三群並無顯著差異。 此外，筆者於本次研究中也對學生問卷調查一些筆者有興趣的相關議題，並進行問卷分析，得到以下結果： 一、對於本研究所編撰「信賴區間」之課程教材，學生普遍能夠接受且瞭解，並知曉「信賴區間」在生活上的用處，且能解讀其資訊。唯實務面上，他們對「信賴區間」之學習則持可有可無的態度。 二、本次研究的授課方式對於自然組與社會組學生的接受程度是具有差異的，其中自然組學生較能接受本次非傳統型的授課方式。 三、學生普遍認為高中數學中，「非統計類數學課程」是比較有趣的，「統計類數學課程」則在學習上具相對困難性。而在統計的課程中，「信賴區間」倒是比較感興趣的這單元。 整體而言，本次研究對學生進行信賴區間的教學結果，是具有學習成效的。 / Based on the 99 Curriculum Guidelines for the Senior High School Math, a special set of study material for Confidence Interval was composed. Eleventh and twelfth grade students from a girl’s senior high school were recruited voluntarily and lectured, and their learning performance were evaluated before and after the completion of the lecture. The primary findings are as the following: 1. Though twelfth grade students have already studied Confidence Interval before the lecture, their pre-test scores were still low. 2. On the average, both eleventh and twelfth grade students performed better after the lecture, and no significant differences were observed between them. 3. For the eleventh grade students, no significant differences were observed between social science and natural science groups. However, students in social science group appeared to work harder, and their post-test results were slightly better than those in natural science group. 4. For the twelfth grade students, significant differences were observed between social science and natural science groups. Natural science group students appeared to outperform their counterparts in social science group. 5. Among the top third, the middle third, and the bottom third of all the participating students, although their pre-test and post-test scores differed significantly, the differences between the two tests were not significant. In addition, some secondary issues were also explored, and the related findings are summarized as follows: 1. Students showed appreciation for the study material, understood the concept of Confidence Interval better after the lecture and even realize how to apply the concept to their daily life. Surprisingly, however, they didn’t think learning Confidence Interval would make any difference in their life. 2. Students in the natural science group appeared to have greater acceptance toward the unconventional teaching method than those in the social science group. 3. For the topics covered in senior high school math, students generally considered those unrelated to statistics more interesting, and thought that statistics-related topics were more difficult to learn. However, among the statistics-related topics, Confidence Interval was the most intriguing one. In conclusion, this study reveals that the experimental teaching approach concerning Confidence Interval are apparently positive and effective.

Benford’s Law states that the first significant digit for most data is not uniformly distributed. Instead, it follows the distribution: P(d = d1) = log10(1 + 1/d1) for d1 ϵ {1, 2, …, 9}. In 2006, my supervisor, Dr. Mary Lesperance et. al tested the goodness-of-fit of data to Benford’s Law using the first significant digit. Here we extended the research to the first two significant digits by performing several statistical tests – LR-multinomial, LR-decreasing, LR-generalized Benford, LR-Rodriguez, Cramѐr-von Mises Wd2, Ud2, and Ad2 and Pearson’s χ2; and six simultaneous confidence intervals – Quesenberry, Goodman, Bailey Angular, Bailey Square, Fitzpatrick and Sison. When testing compliance with Benford’s Law, we found that the test statistics LR-generalized Benford, Wd2 and Ad2 performed well for Generalized Benford distribution, Uniform/Benford mixture distribution and Hill/Benford mixture distribution while Pearson’s χ2 and LR-multinomial statistics are more appropriate for the contaminated additive/multiplicative distribution. With respect to simultaneous confidence intervals, we recommend Goodman and Sison to detect deviation from Benford’s Law.

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No. of bitstreams: 1 arce_cds_me_jabo.pdf: 1179630 bytes, checksum: c8a13228e501d97cb1dd118aca364265 (MD5) Previous issue date: 2018-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Com o avanço dos estudos em genética e da tecnologia aplicada à genotipagem de marcadores moleculares, a identificação de polimorfismos associados às características de interesse econômico se tornou mais acessível, possibilitando a sua utilização aumentar a acurácia de modelos de predição do mérito genético dos animais. Esse avanço também possibilitou aumentar a acurácia dos estudos para identificação de QTLs para características de interesse econômico. Entretanto, os marcadores comumente utilizados para tal fim são os SNPs, que por serem bi-alélicos podem não ser muito eficientes na identificação dos QTLs. Os haplótipos, multi-alélicos, apresentam maior possibilidade de estarem em desequilíbrios de ligação (DL) com os QTLs. Dessa forma, objetivou-se no presente trabalho identificar o melhor método de construção de haplótipos para utilização em estudos de detecção de QTLs, a partir da comparação dos três métodos mais comumente utilizados para este fim. Foram utilizadas três populações simuladas representando características com três diferentes valores de herdabilidade, para as quais foram armazenados os dados fenotípicos, genotípicos e de pedigree dos 6.000 animais da população mais recente: Pop1 com herdabilidade baixa (0,10); Pop2 com herdabilidade moderada (0,25); e, Pop3 com herdabilidade alta (0,35). Os genomas simulados consistiram de 750.000 marcadores do tipo SNP, e 750 QTLs, com dois a quatro alelos, dispostos aleatoriamente em 29 cromossomos com tamanho total de 2.333 centimorgans (cM). A partir da simulação foram eliminados os SNPs cuja frequência do menor alelo foi menor que 0,1, restando 576.027, 577.189 e 576.675 marcadores para as populações Pop1, Pop2 e Pop3, respectivamente. A variação fenotípica foi de 1,0 e a variação dos QTLs foi de 50% das herdabilidades, para cada população. As médias dos DL para cada cromossomo, medidas pela estatística D', variaram de 0,20 até 0,30 para todas as populações, na última geração. Foram construídos haplótipos utilizando três métodos: Intervalo de Confiança (IC), Regra de Quatro Gametas (RQG) e Janelas Sobrepostas (JS). Para Pop1, no cromossomo 15, os métodos IC, RQG e JS identificaram cinco, oito e sete QTLs, respectivamente. Somente um QTL foi identificado nos cromossomos 19 e 29. Para a característica de herdabilidade alta, foi identificado um QTL no cromossomo 11. Em relação às análises de associação utilizando SNPs individuais, foram identificados quatro QTLs no cromossomo 15. Para a característica de herdabilidade moderada, não foram encontrados haplótipos ou SNPs isolados significativos. A metodologia de formação de haplótipos baseado na RQG foi considerada a mais eficiente para detecção de QTLs em relação aos métodos IC e JS, bem como ao uso dos SNPs isolados. / With the advancement of genetic studies and the technology applied to the genotyping of molecular markers, the identification of polymorphisms associated with the characteristics of economic interest became more accessible, allowing its use to increase the accuracy of prediction models of the genetic merit of the animals. This advance also made it possible to increase the accuracy of studies to identify QTLs for characteristics of economic interest. However, the commonly used markers for this purpose are SNPs, which because they are bi-allelic may not be very efficient in identifying QTLs. The haplotypes, multi-allelic, are more likely to be in linkage disequilibrium (LD) with QTLs. Thus, the objective of this work was to identify the best haplotype construction method for use in QTLs detection studies, by comparing the three methods most commonly used for this purpose. Three simulated populations representing characteristics with three different heritability values were used for which the phenotypic, genotypic and pedigree data of the 6,000 animals were stored: Pop1 with low heritability (0.10); Pop2 with moderate heritability (0.25); and, Pop3 with high heritability (0.35). The simulated genomes consisted of 750,000 SNP-type markers, and 750 QTLs, with two to four alleles, arranged randomly on 29 chromosomes with a total size of 2,333 centimorgans (cM). From the simulation the SNPs whose frequency of the lowest allele was less than 0.1 were eliminated, leaving 576,027, 577,189 and 576,675 markers for Pop1, Pop2 and Pop3 populations, respectively. The phenotypic variation was 1.0 and the variation of QTLs was 50% of the heritabilities, for each population. The mean LD for each chromosome, measured by the D' statistic, ranged from 0.20 to 0.30 for all populations in the last generation. Haplotypes were constructed using three methods: Confidence Interval (CI), Four Gametes Rule (FGR) and Sliding-Window (SW). For Pop1, on chromosome 15, CI, FGR and SW methods identified five, eight and seven QTLs, respectively. Only one QTL was identified on chromosomes 19 and 29. For the high heritability characteristic, a QTL was identified on chromosome 11. Regarding the association analyzes using individual SNPs, four QTLs were identified on chromosome 15. For the moderate heritability characteristic, no significant isolated haplotypes or SNPs were found. The methodology of haplotype formation based on the FGR was considered the most efficient for the detection of QTLs in relation to CI and SW methods, as well as to the use of isolated SNPs.