This project is associated with statistical methods to find the unknown parameters of a model. It is the statistical investigation of the algorithm with respect to accuracy (the Cramer-Rao bound and L-curve technique) and optimization of the algorithmic parameters. This project aims to estimate the true temperature (final temperature) of a certain liquid in a container by using initial measurements (readings) from a temperature probe with a known time constant. Basically, the final temperature of the liquid was estimated, before the probe reached its final reading. The probe obeys a simple first-order differential equation model. Based on the model of the probe and the measurement data the estimate was calculated of the ’true’ temperature in the container by using a maximum likelihood approach to parameter estimation.  The initial temperature was also investigated. Modelling, analysis, calculations, and simulations of this problem were explored.

Made available in DSpace on 2016-03-15T19:41:23Z (GMT). No. of bitstreams: 1 Lucia Cunha Lee.pdf: 6101361 bytes, checksum: 97fc5563d800b7ac6a05a73e68ddd500 (MD5) Previous issue date: 2014-06-10 / Fundo Mackenzie de Pesquisa / Parent-child interaction is an important interface in psychological assessment. Mediated Learning Experience (MLE) describes a type of directed interaction that influences the development of the child with whom the adult interacts. It is notewerthy the importance of the mediating function that parents can establish with their children and how it can be affected when the child presents any development disorder. Williams Syndrome is caused by a segmental aneusomy due to the deletion of multiple genes in chromosome region 7q11.23. Some indicators for the diagnosis are identified at birth, such as typical facial features and the presence of cardiac and renal alterations. Among behavioral characteristics, it is observed excessive sociability and a cognitive profile with intelectual disability and discrepancies in the manifestation of cognitive skills, such as impaired visuospatial function and preserved language skills, especially expressive ones. Considering these conditions, the present study aimed at analizing mediating actions taken by mothers during semidirected activities (assembling a puzzle and telling and retelling a story), performed with their daughters who have WS. To do so, it was described how mothers manage mediations with their daughters, based on MLE. Three mother-child dyads took part in the study. There were 5 sessions, two between mother and child and three between the mother and the researcher. During the sessions involving mother and child, it was possible to notice that mothers presented qualitatively and quantitatively varied mediating actions during the tasks, exposing differences according to the type and complexity of tasks (such as giving verbal instructions, using a model for the puzzle, drawing attention to parts of the story). Categories of MLE Scale proved adequate for the assessment steps as they offered an overview of the mediator s actions repertoire. It was verified that the shared experience between mother and daughter was a stimulus and a facilitator to situations of reflexion in individual interviews with the mothers. Thus, the association of observation by the mother, interaction with her daughter and individual interview proved effective to achieve a qualitative alteration of mediation strategies and is also promising for the development of children with WS. Therefore we underline the importance of observation of parental interactions as well as reflection upon them as assessment and intervention tools in the field of development disorders. / A interação de pais e filhos configura-se como uma importante interface na avaliação psicológica. A Experiência de Aprendizagem Mediada (EAM) descreve um tipo de interação dirigida que influencia o desenvolvimento das capacidades da criança com a qual o adulto interage. Vale destacar a importância da função mediadora que os pais podem estabelecer com seus filhos e como essa pode ser afetada quando o filho apresenta algum transtorno em seu desenvolvimento. A Síndrome de Williams (SW) é ocasionada por uma aneusomia segmentar devido à deleção de múltiplos genes na região cromossômica 7q11.23. Alguns indicadores para o diagnóstico da síndrome são identificados desde o nascimento, como as características faciais típicas a presença de alterações cardíacas e renais. Na dimensão relacionada ao comportamento, observa-se excessiva sociabilidade e um perfil cognitivo com deficiência intelectual e discrepâncias na manifestação de habilidades cognitivas, como prejuízos visoespaciais e preservação de habilidades de linguagem, especialmente as expressivas. Com base nesses pressupostos, o presente estudo analisa as ações mediadoras apresentadas por mães a partir de atividades semidirigidas (montar quebra-cabeças e contar e recontar histórias), realizadas com suas filhas que apresentam SW. Para isso, foi descrito como essas mães manejam as mediações com suas filhas, tendo por base a EAM. Participaram desse estudo três díades mãe-criança, em cinco encontros consecutivos, sendo dois entre a mãe e a criança e três entre a mãe e a pesquisadora. Nos encontros com os pares mãe-criança, foi possível notar que diante de tarefas, as mães apresentaram ações mediadoras diversificadas no que diz respeito à quantidade e qualidade, expondo diferenças de acordo com o tipo de atividade e a complexidade das tarefas (como dar instruções verbais, utilizar modelo para o quebra-cabeça, chamar atenção para partes da história). As categorias da Escala EAM revelaram-se apropriadas para etapas de avaliação, oferecendo um levantamento do repertório de ações do mediador. Verificou-se que a experiência compartilhada entre a mãe e a filha foi um estímulo e um facilitador para as situações de reflexão nas entrevistas individuais com as mães. Assim, a associação da observação - por parte da mãe - da interação com a sua filha, com a entrevista individual, indicou ser um dispositivo importante para a modificação qualitativa das estratégias de mediação e promissora no desenvolvimento de suas crianças com SW. Logo, enfatiza-se a importância das observações das interações parentais, além de reflexões dirigidas sobre elas, como um recurso na avaliação e na intervenção na área de transtornos de desenvolvimento.

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In this work, we propose a novel two-component mixture model: the first component is the three-parameter generalized Gaussian distribution (GGD), and the second is a new three-parameter family of positive densities on the real line. The novelty of our mixture model is that we allow the two components to have totally different parametric families of distributions with asymmetric tails of the mixture density. We extend the scale invariant variable fractional moments (SIVFM) method proposed by Song for the GGD to the parameter estimation of our mixture model. We show that the SIVFM population and sample equations for the second component share very similar desirable global properties such as convexity and unique global roots as those for the GGD given in earlier research. The two-component mixing of these properties make the SIVFM mixture population and estimation equations well-behaved resulting in easy to compute estimators without the issue with starting values. The asymptotic results such as consistency and limiting distribution of the estimators are presented. Furthermore, SIVFM estimators can also serve as a consistent initial estimator for the EM algorithm leading to improved accuracy of the EM algorithm. These algorithms are applied to the analysis of the average amount of precipitation (rainfall) for each of 70 United States (and Puerto Rican) cities clearly demonstrating the bimodal distribution of the estimated mixture density.

This Master thesis aims to solve the question of developmentally-creative possibilities in the schooling process. This question is contextualized education of socially disadvantaged pupils. Because in shaping the learning competencies, this area is not developed enough and specific methods are somewhat rigid, it will be introduced one of the option how to to develop learning skills and abilities of the pupils , and which are in the teaching competencies deemed as essential. In this context will be introduced stimulatory and intervention program of Instrumental Enrichment as a concrete form of execution of Mediated learning and also as an effort of perspective innovation of curriculum. With the intention to point out the limitless possibilities of developing pupil's learning potential, the text focuses on the theoretical and conceptual bases, which constitute the entire program. The program is the instrumental set of tools that lead to the activation of cognitive structures and their subsequent enrichment. Therefore, except the theoretical foundations are also presented cognitive strategies metacognitive training that simplify cognitive modifiability, and that lead to the development of pupils' learning potential.

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MSc (Statistics) / Department of Statistics / Daily peak electricity data from ESKOM, South African power utility company for the period, January 1997 to December 2013 consisting of 6209 observations were used in this dissertation. Since 1994, the increased electricity demand has led to sustainability issues in South Africa. In addition, the electricity demand continues to rise everyday due to a variety of driving factors. Considering this, if the electricity generating capacity in South Africa does not show potential signs of meeting the country’s demands in the subsequent years, this may have a significant impact on the national grid causing it to operate in a risky and vulnerable state, leading to disturbances, such as load shedding as experienced during the past few years. In particular, it is of greater interest to have sufficient information about the extreme value of the stochastic load process in time for proper planning, designing the generation and distribution system, and the storage devices as these would ensure efficiency in the electrical energy in order to maintain discipline in the grid systems. More importantly, electricity is an important commodity used mainly as a source of energy in industrial, residential and commercial sectors. Effective monitoring of electricity demand is of great importance because demand that exceeds maximum power generated will lead to power outage and load shedding. It is in the light of this that the study seeks to assess the frequency of occurrence of extreme peak electricity demand in order to come up with a full electricity demand distribution capable of managing uncertainties in the grid system. In order to achieve stationarity in the daily peak electricity demand (DPED), we apply a penalized regression cubic smoothing spline to ensure the data is non-linearly detrended. The R package “evmix” is used to estimate the thresholds using the bounded corrected kernel density plot. The non-linear detrended datasets were divided into summer, spring, winter and autumn according to the calender dates in the Southern Hemisphere for frequency analysis. The data is declustered using Ferro and Segers automatic declustering method. The cluster maxima is extracted using the R package “evd”. We fit Poisson GPD and stationary point process to the cluster maxima and the intensity function of the point process which measures the frequency of occurrence of the daily peak electricity demand per year is calculated for each dataset. The formal goodness-of-fit test based on Cramer-Von Mises statistics and Anderson-Darling statistics supported the null hypothesis that each dataset follow Poisson GPD (σ, ξ) at 5 percent level of significance. The modelling framework, which is easily extensible to other peak load parameters, is based on the assumption that peak power follows a Poisson process. The parameters of the developed i models were estimated using the Maximum Likelihood. The usual asymptotic properties underlying the Poisson GPD were satisfied by the model. / NRF

Ce travail porte sur les séries spatiales. On étudie les phénomènes dont l’observation est un processus aléatoire indexé par un ensemble spatial. Dans cette thèse on s’intéresse aux données bidimensionnelles régulièrement dispersées dans l’espace, on travaille alors dans un rectangle régulier (sur Z2) . Cette modélisation vise donc à construire des représentations des systèmes suivant leurs dimensions spatiales et à ses applications dans de nombreux domaines tels que la météorologie, l’océanographie, l’agronomie, la géologie, l’épidémiologie, ou encore l’économétrie etc. La modélisation spatiale permet d’aborder la question importante de la prédiction de la valeur d’un champ aléatoire en un endroit donné d’une région. On suppose que la valeur à prédire dépend des observations dans les régions voisines. Ceci montre la nécessité de tenir compte, en plus de leurs caractéristiques statistiques, des relations de dépendance spatiale entre localisations voisines, pour rendre compte de l’ensemble des structures inhérentes aux données. Dans la plupart des champs d’applications, on est souvent confronté du fait que l’une des sources majeures de fluctuations est la saisonnalité. Dans nos travaux on s’intéresse particulièrement à ce phénomène de saisonnalité dans les données spatiales. Faire une modélisation mathématique en tenant en compte l’interaction spatiale des différents points ou localités d’une zone entière serait un apport considérable. En effet un traitement statistique qui prendrait en compte cet aspect et l’intègre de façon adéquat peut corriger une perte d’information, des erreurs de prédictions, des estimations non convergentes et non efficaces. / This thesis focuses on the time series in addition to being observed over time, also have a spatial component. By definition, a spatiotemporal phenomenon is a phenomenon which involves a change in space and time. The spatiotemporal model-ling therefore aims to construct representations of systems taking into account their spatial and temporal dimensions. It has applications in many fields such as meteorology, oceanography, agronomy, geology, epidemiology, image processing or econometrics etc. It allows them to address the important issue of predicting the value of a random field at a given location in a region. Assume that the value depends predict observations in neighbouring regions. This shows the need to consider, in addition to their statistical characteristics, relations of spatial dependence between neighbouring locations, to account for all the inherent data structures. In the exploration of spatiotemporal data, refinement of time series models is to explicitly incorporate the systematic dependencies between observations for a given region, as well as dependencies of a region with neighboring regions. In this context, the class of spatial models called spatiotemporal auto-regressive models (Space-Time Autoregressive models) or STAR was introduced in the early 1970s. It will then be generalized as GSTAR model (Generalized Space-Time Autoregressive models). In most fields of applications, one is often confronted by the fact that one of the major sources of fluctuations is seasonality. In our work we are particularly interested in the phenomenon of seasonality in spatiotemporal data. We develop a new class of models and investigates the properties and estimation methods. Make a mathematical model taking into account the spatial inter-action of different points or locations of an entire area would be a significant contribution. Indeed, a statistical treatment that takes into account this aspect and integrates appropriate way can correct a loss of information, errors in predictions, non-convergent and inefficient estimates.

風險值大多是在假設資產報酬為常態分配下計算而得的，但是這個假設與實際的資產報酬分配不一致，因為很多研究者都發現實際的資產報酬分配都有厚尾的現象，也就是極端事件的發生機率遠比常態假設要來的高，因此利用常態假設來計算風險值對於真實損失的衡量不是很恰當。 針對這個問題，本論文以歷史模擬法、變異數-共變異數法、混合常態模型來模擬報酬率的分配，並依給定的信賴水準估算出風險值，其中混合常態模型的參數是利用準貝式最大概似估計法及EM演算法來估計；然後利用三種風險值的評量方法：回溯測試、前向測試與二項檢定，來評判三種估算風險值方法的優劣。 經由實證結果發現： 1.報酬率分配在左尾臨界機率1％有較明顯厚尾的現象。 2.利用混合常態分配來模擬報酬率分配會比另外兩種方法更能準確的捕捉到左尾臨界機率1％的厚尾。 3.混合常態模型的峰態係數值接近於真實報酬率分配的峰態係數值，因此我們可以確認混合常態模型可以捕捉高峰的現象。 關鍵字：風險值、厚尾、歷史模擬法、變異數-共變異教法、混合常態模型、準貝式最大概似估計法、EM演算法、回溯測試、前向測試、高峰 / Initially, Value at Risk (VaR) is calculated by assuming that the underline asset return is normal distribution, but this assumption sometimes does not consist with the actual distribution of asset return. Many researchers have found that the actual distribution of the underline asset return have Fat-Tail, extreme value events, character. So under normal distribution assumption, the VaR value is improper compared with the actual losses. The paper discuss three methods. Historical Simulated method - Variance-Covariance method and Mixture Normal .simulating those asset, return and VaR by given proper confidence level. About the Mixture Normal Distribution, we use both EM algorithm and Quasi-Bayesian MLE calculating its parameters. Finally, we use tree VaR testing methods, Back test、Forward tes and Binomial test -----comparing its VaR loss probability We find the following results: 1.Under 1% left-tail critical probability, asset return distribution has significant Fat-tail character. 2.Using Mixture Normal distribution we can catch more Fat-tail character precisely than the other two methods. 3.The kurtosis of Mixture Normal is close to the actual kurtosis, this means that the Mixture Normal distribution can catch the Leptokurtosis phenomenon. Key words: Value at Risk、VaR、Fat tail、Historical simulation method、 Variance-Covariance method、Mixture Normal distribution、Quasi-Bayesian MLE、EM algorithm、Back test、 Forward test、 Leptokurtosis

Mother-Tongue-Based Multilingual Education (MTB MLE) has become an important concept in the field of primary education in many parts of the world. MTB MLE is a form of education that deals with the bridging of learning in the mother tongue to using one or more languages as languages of instruction in schools. This study took place in the Southern Nation and Nationality Peoples Regional State of Ethiopia (SNNPRS) to investigate the implementation challenges faced by two sample minority languages, namely Dawuro and Kontaatho, that use the mother tongue as both medium of instruction and as a subject in primary schools. The study focused on the drawbacks that hindered the proper implementation of the education and training policy regarding mother-tongue education in minority language areas. To conduct the study, the qualitative research method was employed. Representatives from the Ministry of Education, Colleges of Teacher Education, primary school directors and teachers of mother tongue as a subject and as a medium of instruction, parents and relevant community representatives took part. From the Ministry of Education, two experts from the Curriculum Design and Implementation Directorate and two participants from Mother tongue and English Language development directorate were purposively invited to participate in individual interviews. Similarly, three instructors from one of the Colleges of Teacher Education and 32 mother-tongue teachers drawn from eight schools of the target area were also individually interviewed. In addition, three heterogenous focus group discussions were conducted with stakeholders comprising community and parents’ representatives, schoolteachers’ representative, students’ representatives and school directors. The study was based on the social constructivist and Vygotsky’s Zone of Proximal Development theoretical assumptions. The findings of the study indicated that MTB MLE is not being successfully implemented in the minority language areas in the SNNPRS because of the deficits in awareness raising, proper teacher training, readiness of the languages in relation to orthography and scientific terminology to be used as medium of instruction, availability and quality of teaching and learning materials, standardised orthography, availability of guidelines and a strategy to carry out the MTB MLE programme, support and follow up of the implementation of the MTB MLE programme. / Curriculum and Instructional Studies / Ph. D. (Curriculum and Instructional Studies)