This work deals with two Monte Carlo simulation studies in log-symmetric regression models, which are particularly useful for the cases when the response variable is continuous, strictly positive and asymmetric, with the possibility of the existence of atypical observations. In log- symmetric regression models, the distribution of the random errors multiplicative belongs to the log-symmetric class, which encompasses log-normal, log- Student-t, log-power- exponential, log-slash, log-hyperbolic distributions, among others. The first simulation study has as objective to examine the performance for the maximum-likelihood estimators of the model parameters, where various scenarios are considered. The objective of the second simulation study is to investigate the accuracy of popular information criteria as AIC, BIC, HQIC and their respective corrected versions. As illustration, a movie data set obtained and assembled for this dissertation is analyzed to compare log-symmetric models with the normal linear model and to obtain the best model by using the mentioned information criteria.

Nearly half of the natural disasters in the world are due to hydro-geomorphological hazards. Therefore, rainfall forecast is a key parameter for the implementation of landslides and flash-floods early warning systems. In this work we developed a routine in R software that enables the validation of a 3-day rainfall forecast by comparison with the daily rainfall data recorded in 101 automatic meteorological stations available in mainland Portugal. The routine integrates the pre-processing of base data, the matching between the 3-day rainfall forecast and the daily rainfall registered in the automatic meteorological stations based on sequence of days, the estimation of the difference between the forecasted and the real rainfall values and the computation of error measures, such as the bias, the mean absolute error, the mean absolute percentage error and the root mean square error. The results from the error measures, estimated for the 101 automatic meteorological stations, are then exported to an excel file. The routine is implemented for mainland Portugal and tested using data from February 2015, however, the spatial and temporal data can be easily updated for other regions. A routine to validate the rainfall forecast at the regional scale using R programming language is implemented. The automated routine can be easily updated and adapted with different spatial and temporal scales.

A Regressão é uma técnica estatística utilizada na investigação da relação entre variáveis que surgem em problemas das mais variadas áreas da ciência. De uma forma geral, o investigador procura aferir a influência de uma variável explicativa X sobre o valor esperado de uma variável de resposta denominada Y. Por exemplo, qual o efeito do aumento de preços na procura; qual o efeito da pressão sanguínea no risco de acidente cardiovascular ou qual o efeito das descargas na probabilidade de cheia. Os modelos de regressão são vários e são definidos consoante o número de variáveis explicativas, cujos efeitos na variável Y, que se pretendem estudar. Nesta dissertação, serão abordados os modelos de regressão linear simples, Regressão linear múltipla e logística através do software estatístico R em problemas de contexto real no âmbito da análise do risco.

The distribution of the product of two normally distributed random variables has been an open problem from the early years in the XXth century. First approaches tried to determinate the mathematical and statistical properties of the distribution of such a product using different types of functions. Recently, an improvement in computational techniques has performed new approaches for calculating related integrals by using numerical integration. Another approach is to adopt any other distribution to approximate the probability density function of this product. The skew-normal distribution is a generalization of the normal distribution which considers skewness making it flexible. In this work, we approximate the distribution of the product of two normally distributed random variables using a type of skew-normal distribution. The influence of the parameters of the two normal distributions on the approximation is explored. When one of the normally distributed variables has an inverse coefficient of variation greater than one, our approximation performs better than when both normally distributed variables have inverse coefficients of variation less than one. A graphical analysis visually shows the superiority of our approach in relation to other approaches proposed in the literature on the topic.

In this work the probability density function (PDF) for the product of two uniformly distributed random variables is explored under the implementation of a new procedure in R language. Based on the Rohatgi theorem for the theoretical form of the product, different possibilities for the range of values of the limits of both distributions are considered. As an application, the management of a (Q,r) inventory model with the presence of lead-time and uniform demand forecasts is considered. Solution to this model looks up to minimize the total costs through the variables Q (reorder quantity) and r (the reorder point), and not always exists an analytical solution of the problem. We show a graphical procedure for the simulation results and a more exactly analytical solution. Implementation in R is straightforward.

In this article, we introduce charts for attribute control considering the number of defective items, named np‐charts. These charts are preferable over charts for proportion (p) of defective items, named p‐charts, when the sample size (n) remains constant for all subgroups. The benefits of using np‐charts over p‐charts are: an easier interpretation and the fact that no calculation is required for each sample result. We provide a review of the basic issues related to np‐charts and some recent ideas on the topic based on life distributions. In addition, we discuss an implementation of np‐charts in the R software by using examples with data on attributes and lifetimes.

Considering the implementation of an Experimental Design, in any field, the experimenter must pay particular attention and look for the best strategies in the following steps: planning the design selection, conduct the experiments, collect observed data, proceed to analysis and interpretation of results. The focus is on providing both - a deep understanding of the problem under research and a powerful experimental process at a reduced cost. Mainly thanks to the possibility of allowing to separate variation sources, the importance of Experimental Design in Health Sciences is strongly recommended since long time. Particular attention has been devoted to Block Designs and more precisely to Balanced Incomplete Block Designs - in this case the relevance states from the fact that these designs allow testing simultaneously a number of treatments bigger than the block size. Our example refers to a possible study of inter reliability of the Parkinson disease, taking into account the UPDRS (Unified Parkinson’s disease rating scale) in order to test if there are significant differences between the specialists who evaluate the patients performances. Statistical studies on this disease were described for example in Richards et al (1994), where the authors investigate the inter-rater Reliability of the Unified Parkinson’s Disease Rating Scale Motor Examination. We consider a simulation of a practical situation in which the patients were observed by different specialists and the UPDRS on assessing the impact of Parkinson’s disease in patients was observed. Assigning treatments to the subjects following a particular BIBD(9,24,8,3,2) structure, we illustrate that BIB Designs can be used as a powerful tool to solve emerging problems in this area. Once a structure with repeated blocks allows to have some block contrasts with minimum variance, see Oliveira et al. (2006), the design with cardinality 12 was selected for the example. R software was used for computations.

Large volumes of data are becoming increasingly available and can be very valuable for the analysis of different phenomena. These data can originate from multiple sources and be recorded in diverse formats, requiring preliminary scrutiny in order to be further used in scientific analyses. This first crucial phase of filtering and cleansing data is usually a cumbersome and time-consuming task, but automated routines can be developed to help researchers. A routine created with the R language is here presented, to screen, harmonize and aggregate international trade data, representing the trade flows between countries for specific products, in a timeframe that covers monthly flows for at least 15 years for most countries. The R script implementing these routines is provided, being easily adapted to other datasets with similar issues. • A step-by-step procedure for cleansing and harmonizing international trade data, using R programming language, is presented • Automated routines are very effective in obtaining robust and filtered data inputs to integrate in scientific models • Spatial and temporal patterns of worldwide trade relations can be explored to enhance our understanding of various associated phenomena

Para disponibilizar um sistema de fornecimento de dados que objetivando-se subsidiar pesquisas de Melhoramento Genético Animal direcionadas à comparação de metodologias de avaliação genética, foi avaliado o comportamento da variância genética aditiva de populações selecionadas e não selecionadas, por seis gerações sucessivas, via simulação Monte Carlo. Por meio de um modelo genético aditivo, foram simuladas populações de 40 animais (20 machos e 20 fêmeas), sob seleção e acasalamento aleatório. Da geração zero até a quinta geração notou-se na população selecionada uma redução de 44,4% na variância genética aditiva, devido a um aumento de 11,58% no coeficiente de endogamia. Na população não selecionada a redução da variância genética aditiva foi menor (27,46%) em relação à população selecionada, também devido a aumento de 10,26% no coeficiente de endogamia.

A análise conjunta de variáveis qualitativas e quantitativas tem sido apontada como ferramenta útil na estimativa da divergência genética entre os acessos de uma coleção de germoplasma. O presente trabalho teve como objetivos caracterizar uma coleção de germoplasma de tomateiro do grupo cereja, com base em descritores qualitativos e quantitativos e utilizar o algoritmo de Gower na quantificação da divergência genética. Estudaram-se 40 acessos de tomateiro cereja, cultivados em manejo orgânico nas condições de Seropédica, Estado do Rio de Janeiro. Foram utilizados quatro descritores qualitativos relacionados aos frutos e nove descritores quantitativos. Os dados foram analisados de forma conjunta pelo algoritmo de Gower. Detectou-se variabilidade para coloração, formato e número de lóculos do fruto. A coloração vermelha foi observada em 25 acessos testados, registrando-se também a produção de frutos amarelos, laranjas e marrons. Para número de lóculos, foi registrada a ocorrência de frutos bi, tri, tetra e pluriloculares (com até sete lóculos). O método UPGMA foi o que obteve o maior coeficiente de correlação cofenética (0,80), observando-se a formação de sete grupos. Os grupos formados permitiram a distinção de frutos classificados como cereja e outros que não se adequaram a esta definição, por estarem acima do diâmetro equatorial proposto para esta classe.