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The role of Experimental Design is very well known, considering applications to a broad range of areas, such as Agriculture, Biology, Medicine, Industry, Education, Economy, Engineering and Food Consumption Sciences. Motivated by the variety of problems faced in the several areas and simultaneously taking advantage of the emerging technological developments, new theoretical results, as well as new designs and structures, have been developed by researchers and practitioners accordingly to the needs. Experimental Design got a place among the most important statistical methodologies and, mainly because of allowing to separate variation sources, since the last century it has been strongly recommended for Health Sciences studies. In this area, particular attention has been devoted to Randomized Complete Block Designs and to Balanced Incomplete Block Designs (BIBD) - which allow testing simultaneously a number of treatments bigger than the block size. Thus, after a brief review of some particular BIBD properties and of BIBDR - Balanced Incomplete Blocks with Block Repetition, an applications to Health Sciences simulated data is illustrated, by exploring R software. [ABSTRACT FROM AUTHOR]

This paper presents a study of the evolution the study of the product of two normally distributed variables. From first approaches in the middle of the 20th Century until the most recent ones from this decade. Nowadays, existence of an unique formula for the product was not proved. Partial results using different approaches: Bessel Functions, Numerical Integration, Pearson Type Function, … [ABSTRACT FROM AUTHOR]

Kurtosis (k) is any measure of the "peakedness" of a distribution of a real-valued random variable. We study the evolution of the Kurtosis for the product of two normally distributed variables. Product of two normal variables is a very common problem for some areas of study, like, physics, economics, psychology, … Normal variables have a constant value for kurtosis (k = 3), independently of the value of the two parameters: mean and variance. In fact, the excess kurtosis is defined as k-3 and the Normal Distribution Kurtosis is zero. The product of two normally distributed variables is a function of the parameters of the two variables and the correlation between then, and the range for kurtosis is in [0;6] for independent variables and in [0;12] when correlation between then is allowed. [ABSTRACT FROM AUTHOR]

The observation of certain higher chemical element concentration, such as uranium and radiometric values, in the Alegrete-Assumar region of Portugal, has shown that locally occurrence of radioactive quartzites is responsible for these high values. The geostatistical treatment of exploration data and the crossing of the database with other variables, such as land use, allows one to study how these may affect the human health. [ABSTRACT FROM AUTHOR]

The distribution of the ratio of two normal random variables X and Y was studied from [1] (the density function) and [2] (the distribution function). The shape of its density function can be uni-modal, bimodal, symmetric, asymmetric, following several type of distributions, like Dirac Distribution, Normal Distribution, Cauchy Distribution or Recinormal Distribution. In this paper we study a different approximation for this distribution Z = X/Y, as a function of four parameters: ratio of the means of the two normal variables, ratio of the standard deviations of the two normal variables, the variation coefficient of the normal variable Y, and the correlation between the two variables. A formula for the Distribution function and the density function of Z is given. In addition, using graphical procedures we established singularity points for the parameters where the approximation given for Z has a non normal shape. [ABSTRACT FROM AUTHOR]

Big Data has become the new slang in the world of information collection and analysis. The researches we conduct and the data we collect continue to grow, due to rapidly expansion of technology. Disciplines such as Computer Science, Engineering, and Statistics play a key role in the analysis of big data, each with its specificity but all equally important, an opinion that is not shared by all, being the Statistic considered the weakest link. This work attempts to show that Statistics have a distinct and essential role in this new world of Big Data, showing that Statistics and Big Data denote a crucial union. We will start with a brief introduction to Big Data and the several existing definitions. [ABSTRACT FROM AUTHOR]

The existence of Hadamard matrices remains one of the most challenging open questions in combinatorics. Substantial progress on their existence has resulted from advances in algebraic design theory using deep connections with linear algebra, abstract algebra, finite geometry, number theory, combinatorics and optimization. The construction and analysis of Hadamard matrices, and their use on combinatorial designs, play an important role nowadays in diverse fields such as: quantum information, communications, networking, cryptography, biometry and security. Hadamard Matrices are present in our daily life and they give rise to a class of block designs named Hadamard configurations. Different applications of it based on new technologies and codes of figures such as QR Codes are present almost everywhere. Balanced Incomplete Block Designs (BIBD) are very well known as a tool to solve emerging problems in this area. Illustrations and applications to authentication codes and secret sharing schemes will be presented. [ABSTRACT FROM AUTHOR]

The Item Response Theory (IRT) has become one of the most popular scoring frameworks for measurement data, frequently used in computerized adaptive testing, cognitively diagnostic assessment and test equating. According to Andrade et al. (2000), IRT can be defined as a set of mathematical models (Item Response Models - IRM) constructed to represent the probability of an individual giving the right answer to an item of a particular test. The number of Item Responsible Models available to measurement analysis has increased considerably in the last fifteen years due to increasing computer power and due to a demand for accuracy and more meaningful inferences grounded in complex data. The developments in modeling with Item Response Theory were related with developments in estimation theory, most remarkably Bayesian estimation with Markov chain Monte Carlo algorithms (Patz & Junker, 1999). The popularity of Item Response Theory has also implied numerous overviews in books and journals, and many connections between IRT and other statistical estimation procedures, such as factor analysis and structural equation modeling, have been made repeatedly (Van der Lindem & Hambleton, 1997). As stated before the Item Response Theory covers a variety of measurement models, ranging from basic one-dimensional models for dichotomously and polytomously scored items and their multidimensional analogues to models that incorporate information about cognitive sub-processes which influence the overall item response process. The aim of this work is to introduce the main concepts associated with one-dimensional models of Item Response Theory, to specify the logistic models with one, two and three parameters, to discuss some properties of these models and to present the main estimation procedures. [ABSTRACT FROM AUTHOR]

Teaching is a complex mission that requires not only the theoretical knowledge transmission, but furthermore requires to provide the students the necessary skills for solving real problems in their respective professional activities where complex issues and problems must be frequently faced. Over more than twenty years we have been experiencing an increase in scholar failure in the scientific area of mathematics, which means that Teaching Mathematics and related areas can be even a more complex and hard task. Scholar failure is a complex phenomenon that depends on various factors as social factors, scholar factors or biophysical factors. After numerous attempts made in order to reduce scholar failure our goal in this paper is to understand the role of "Problem Based Learning" and how this methodology can contribute to the solution of both: increasing mathematical courses success and increasing skills in the near future professionals in Portugal. Before designing a proposal for applying this technique in our institutions, we decided to conduct a survey to provide us with the necessary information about and the respective advantages and disadvantages of this methodology, so this is the brief review aim. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper we review Stochastic Response Surface Methodology as a tool for modeling uncertainty in the context of Risk Analysis. An application in the survival analysis in the breast cancer context is implemented with R software. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present the fundamentals of game theory and illustrate how the theory can be applied in education of Mathematics. Literature specific applications of game theory across all levels of instructor-led education. With a game theory model, we provide a mathematical description of a social situation in which two or more individuals or players interact. We strongly suggestthat traditional teaching techniques of mathematics should be complemented with games. [ABSTRACT FROM AUTHOR]

The present work aims to propose a systematic study and interpretation of a variable response in relation to three factors, using a model of Joint Table Analysis, the Tucker3 model, as well as the joint biplot graph. The proposed method seems efficient and suitable for separating standard technical response, and the pattern of noise contained in a three inputs table, as well as allows its interpretation. The joint plot graph facilitates the study and interpretation of the data structure and provides additional information on these. In our application the aim is to identify the combinations of genotypes, locations and years that contribute or not to a high yield of bean cultivars. [ABSTRACT FROM AUTHOR]