Theoretical considerations and empirical results show that the one-dimensional quality of non-uniform random numbers is bad and the discrepancy is high when they are generated by the ratio of uniforms method combined with linear congruential generators. This observation motivates the suggestion to replace the ratio of uniforms method by transformed rejection (also called exact approximation or almost exact inversion), as the above problem does not occur for this method. Using the function $G(x) =\left( \frac(a)(1-x)+b\right)x $ with appropriate $a$ and $b$ as approximation of the inverse distribution function the transformed rejection method can be used for the same distributions as the ratio of uniforms method. The resulting algorithms for the normal, the exponential and the t-distribution are short and easy to implement. Looking at the number of uniform deviates required, at the code length and at the speed the suggested algorithms are superior to the ratio of uniforms method and compare well with other algorithms suggested in literature. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Thesis (Ph. D.)--Cornell University, May, 2007. / Vita. Includes bibliographical references (leaves 129-141).

Submitted by Leonardo Oliveira Buturi (leobuturi@gmail.com) on 2018-07-17T16:21:41Z No. of bitstreams: 1 Dissertação Profmat - Leonardo Buturi - alterada.pdf: 1686348 bytes, checksum: 8e0b727cbf88ce5a17eec6b1ed68c981 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-07-17T18:02:15Z (GMT) No. of bitstreams: 1 buturi_lo_me_sjrp.pdf: 1753373 bytes, checksum: 3ba02802ac4746292b08c145040278aa (MD5) / Made available in DSpace on 2018-07-17T18:02:16Z (GMT). No. of bitstreams: 1 buturi_lo_me_sjrp.pdf: 1753373 bytes, checksum: 3ba02802ac4746292b08c145040278aa (MD5) Previous issue date: 2018-06-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Tendo por finalidade apresentar um estudo conciso em alguns tópicos de Estatística, com ênfase em aplicações e na distribuição normal, este trabalho destina-se a alunos e professores do Ensino Médio, que tenham interesse em se aprofundar no estudo destes tópicos. Técnicas estatísticas, principalmente nos problemas que podem ser modelados utilizando-se a distribuição normal, são de interesse geral e muito utilizado nas áreas de biologia, ecologia, administração de empresas e negócios. Inicialmente, são apresentados vários conceitos de Estatística tais como gráficos, medidas de posição e dispersão, conceitos de probabilidade, a distribuição normal, intervalos de confiança para a posterior aplicação em dados envolvendo os preço de combustíveis e notas de alunos dos Ensinos Fundamental e Médio. Os tópicos são expostos de forma que seja acessível aos alunos do ensino médio e as aplicações são motivadoras para a utilização posterior das técnicas apresentadas / Having as purpose present a concise study on Statistics and Probability, with emphasis on applications and the normal distribution, this work is intended for students and High School teachers, who have an interest in deepening on these topics. Statistical techniques, mainly in problems that can be modeled using the normal distribution are of general interest and widely used in the areas of biology, ecology, business administration and business. Initially, are presented several concepts of Statistics such as position and dispersion measurements, probability concepts, normal distribution, simple confidence intervals and applications. Topics are exposed in a way that is accessible to high school students and the applications are motivating for the later use of the techniques presented. / 5566715

>Magister Scientiae - MSc / The problem of optimal investment has been extensively studied by numerous researchers in order to generalize the original framework. Those generalizations have been made in different directions and using different techniques. For example, Perera [Optimal consumption, investment and insurance with insurable risk for an investor in a Levy market, Insurance: Mathematics and Economics, 46 (3) (2010) 479-484] applied the martingale approach to obtain a closed form solution for the optimal investment, consumption and insurance strategies of an individual in the presence of an insurable risk when the insurable risk and risky asset returns are described by Levy processes and the utility is a constant absolute risk aversion. In another work, Sattinger [The Markov consumption problem, Journal of Mathematical Economics, 47 (4-5) (2011) 409-416] gave a model of consumption behavior under uncertainty as the solution to a continuous-time dynamic control problem in which an individual moves between employment and unemployment according to a Markov process. In this thesis, we will review the consumption models in the above framework and will simulate some of them using an infinite series expansion method − a key focus of this research. Several numerical results obtained by using MATLAB are presented with detailed explanations.

Let (X, Y) be bivariate normal random vectors which represent the responses as a result of Treatment 1 and Treatment 2. The statistical inference about the bivariate normal distribution parameters involving missing data with both treatment samples is considered. Assuming the correlation coefficient ρ of the bivariate population is known, the MLE of population means and variance (ξ, η, and σ2) are obtained. Inferences about these parameters are presented. Procedures of constructing confidence interval for the difference of population means ξ – η and testing hypothesis about ξ – η are established. The performances of the new estimators and testing procedure are compared numerically with the method proposed in Looney and Jones (2003) on the basis of extensive Monte Carlo simulation. Simulation studies indicate that the testing power of the method proposed in this thesis study is higher.

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The focus in this thesis is on the calculations of an empirical null distributionfor likelihood ratio tests testing either separable or double separable covariancematrix structures versus an unstructured covariance matrix. These calculationshave been performed for various dimensions and sample sizes, and are comparedwith the asymptotic χ2-distribution that is commonly used as an approximative distribution. Tests of separable structures are of particular interest in cases when data iscollected such that more than one relation between the components of the observationis suspected. For instance, if there are both a spatial and a temporalaspect, a hypothesis of two covariance matrices, one for each aspect, is reasonable.

The low grades that students score in some statistical units in Kenyan universities is of great concern and has evoked research interest in the teaching of some of the units and the students’ learning of the statistical content. The aim of the study was to investigate the difficulties undergraduate students experience in the learning of bivariate normal distribution in a Kenyan university. The research also aimed to answer the following research questions on the difficulties undergraduate students encounter in the learning of bivariate normal distribution. The first research question was based on the reasons why students find learning of bivariate normal distribution difficult and the second research question was to find the reasons why students experience such difficulties in learning bivariate normal distribution. The target population for this study included lecturers teaching statistics in the university, and second- and third- year students enrolled or who have previously completed the probability and statistics III unit, where the bivariate normal distribution content is covered. In selecting students for the study, the simple random sampling technique was employed while convenient sampling was used to select lecturers who participated in the study. A mixed methods design was adopted for this study where both quantitative and qualitative data was collected. A total of 175 students and six lecturers participated in this research study. All students who participated in the study did a bivariate normal distribution test (Appendix 1) designed by the researcher and then filled in a questionnaire (Appendix 2). The lecturers who participated in the study filled in an open-ended questionnaire (Appendix 3). The results showed that undergraduate students have difficulties in learning bivariate normal distribution. This is because most of them could neither state the bivariate normal distribution nor solve any of the application questions on the content. The students find it difficult to learn and comprehend the bivariate normal distribution equation with its many parameters and constants of the two random independent variables. The results also showed that students could not state the normal distribution equation nor could they solve questions on the normal distribution, which forms the foundational knowledge required for effective learning of the bivariate normal distribution content. ii Based on the results, the study recommended that emphasis should be placed on the basic and foundational knowledge of the normal distribution content and its applications before teaching bivariate normal distribution in probability and statistics III. In addition, it is recommended that all students should be involved in the learning of basic content to enable them to understand all parameters and constants in the equations and their applications. The study also recommends that lecturers revise the foundational knowledge and content related to the bivariate normal distribution before introducing and teaching the bivariate normal distribution content. This study also recommends that the university should consider a change of curriculum by teaching the bivariate normal distribution, as an introductory course to the unit under the multivariate distributions in statistics, in third year of the students’ studies. ; ; / Mathematics Education / M. Sc. (Mathematics Education)

Master of Science / Department of Computing and Information Sciences / David A. Gustafson / Octant analysis, when combined with properties of the multivariate central limit theorem and multivariate normal distribution, allows finding a reasonable grasping point on an unknown novel object possible. This thesis’s original contribution is the ability to find progressively improving grasp points in a poor and/or sparse point cloud. It is shown how octant analysis was implemented using common consumer grade electronics to demonstrate the applicability to home and office robotics. Tests were carried out on three novel objects in multiple poses to determine the algorithm’s consistency and effectiveness at finding a grasp point on those objects. Results from the experiments bolster the idea that the application of octant analysis to the grasping point problem seems promising and deserving of further investigation. Other applications of the technique are also briefly considered.