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- Evaluation of kurtosis into the product of two normally distributed variablesPublication . Oliveira, Amilcar; Oliveira, Teresa; Seijas-Macias, J. AntonioKurtosis (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.
- The Mixed CUSUM-EWMA (MCE) control chart as a new alternative in the monitoring of a manufacturing processPublication . Oliveira, Amilcar; Oliveira, Teresa A.; Paladini, Edson Pacheco; Walter, Olga Maria Formigoni Carvalho; Henning, Elisa; Konrath, Andréa Cristina; Alves, Custodio da CunhaGoal: The objective is to conclude, based on a comparative study, if there is a significant difference in sensitivity between the application of MCE and the individual application of the CUSUM or EWMA chart, i.e., greater sensitivity particularly for cases of lesser magnitude of change. Design/Methodology/Approach: These are an applied research and statistical techniques such as statistical control charts are used for monitoring variability. Results: The results show that the MCE chart signals a process out of statistical control, while individual EWMA and CUSUM charts does not detect any situation out of statistical control for the data analyzed. Limitations: This article is dedicated to measurable variables and individual analysis of quality characteristics, without investing in attribute variables. The MCE chart was applied to items that are essential to the productive process development being analysed. Practical Implications: The practical implications of this study can contribute to: the correct choice of more sensitive control charts to detect mainly small changes in the location (mean) of processes; provide clear and accurate information about the fundamental procedures for the implementation of statistical quality control; and encourage the use of this quality improvement tool. Originality/Value: The MCE control chart is a great differential for the improvement of the quality process of the studied company because it goes beyond what CUSUM and EWMA control charts can identify in terms of variability.
- Acid phosphatase, some genetic polymorphism and obesity risk factors in adult womenPublication . Carolino, E.; Oliveira, T.; Silva, A. P.; Carvalho, R; Bicho, M.Recent works point out to a relation between some genetic factors and the predisposition for obesity. We believe, therefore, to be relevant to conduct this kind of study in the Portuguese population. In the present work the following genetic factors are considered: Haptoglobin phenotype, the Acid Phosphatasehenotype and two blood group systems, the MN System and the Lewis System. In addition, it was also considered one demographic factor, age, and one enzymatic activity, the Acid Phosphatase Activity. Haptoglobin (Hp) is a hemoglobin-binding protein of the immune system expressed by a genetic polymorphism with three major phenotypes. This protein is associated in some works with susceptibility for common pathological situations, such as some disorders related with obesity. The Acid phosphatase, more precisely the Acid phosphatase locus 1 (ACP1), is a highly polymorphic enzyme that has an important role in flavoenzyme activity and in the control of insulin receptor activity. High ACP1 activity was positively associated with high glycemic levels and with high body mass index (BMI) values. The MN blood system is a blood group system with three phenotypes each one showing different associations with some diseases, including some related with obesity. Finally, the Lewis System was focused on a single locus with two antigens, Le a and Le b. Confirming this characteristic as a genetic marker of obesity may contribute to the explanation of individual differences in the prevalence of obesity. The group under study involves 85 Portuguese adult women with complete data for all variables, taken from a data base with 714 subjects from the Genetic Laboratory, Centre of Endocrinology and Metabolism of University of Lisbon. The aim of the study is to explore and examine the relationship between the weight categories and the explanatory variables, with emphasis on risk for obesity. Therefore, an ordinal regression model was tried, considering as the regressor variables the Haptoglobin phenotype, Acid phosphatase (ACP1) phenotype, MN blood group system, Lewis system, the enzymatic activity of ACP1, age and some association effects between these factors. Some significant main effects were found at a 5% significance level: the phenotypeLe(a-b+) of Lewis System (p-value=0,021) and age (p-value=0,002). The phenotype Le(a-b+) of Lewis System is associated with a decreased risk for obesity (odds ratio 0,139; CI95%(0,016; 0,754)); age (as expected) is associated with an increased risk for obesity (odds ratio 1,11; CI95%(1,038; 1,190))
- The presence of distortions in the extended skew : normal distributionPublication . Seijas-Macias, J. Antonio; Oliveira, Amilcar; Oliveira, TeresaIn the last years, a very interesting topic has arisen and became the research focus not only for many mathematicians and statisticians, as well as for all those interested in modeling issues: The Skew normal distributions’ family that represents a generalization of normal distribution. The first generalization was developed by Azzalini in 1985, which produces the skew-normal distribution, and introduces the existence of skewness into the normal distribution. Later on, the extended skew-normal distribution is defined as a generalization of skew-normal distribution. These distributions are potentially useful for the data that presenting high values of skewness and kurtosis. Applications of this type of distributions are very common in model of economic data, especially when asymmetric models are underlying the data. Definition of this type of distribution is based in four parameters: location, scale, shape and truncation. In this paper, we analyze the evolution of skewness and kurtosis of extended skew-normal distribution as a function of two parameters (shape and truncation). We focus in the value of kurtosis and skewness and the existence of arange of values where tiny modification of the parameters produces large oscillations in the values. The analysis shows that skewness and kurtosis present an instability development for greater values of truncation. Moreover, some values of kurtosis could be erroneous. Packages implemented in software R confirm the existence of a range where value of kurtosis presents a random evolution.
- Satellite meeting ISI-committee on risk analysis and XI Workshop on Statistics, Mathematics and Computation: book of abstractsPublication . Oliveira, Teresa; Oliveira, Amilcar; Grilo, Luís; Carapau, Fernando; Dias, Cristina; Santos, CarlaThis Book includes the abstracts of the talks presented at the 2017 Satellite Meeting ISI-CRA in honour of Professor David Banks, jointly with the 11th Workshop on Statistics, Mathematics and Computation (WSMC11), hosted at the Politechnic Institute of Portalegre and Universidade Aberta. The location of the meeting was at Universidade Aberta in Lisbon and Politechnic Institute of Portalegre in Portalegre.The meeting organizers celebrated the continued success of WSMC12 and the Satellite Meeting of ISI-CRA. The Executive Committee was constituted by: Teresa Oliveira (Portugal), Lidia Filus (USA), Christos Kitsos (Greece) and M. Ivette Gomes (Portugal).
- Stochastic response surface methodology: a study in the human health areaPublication . Oliveira, Teresa; Leal, Maria da Conceição Dias; Oliveira, AmilcarIn 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.
- Microarray experiments on risk analysis using RPublication . Oliveira, Teresa A.; Oliveira, Amilcar; Monteiro, Andreia A.The microarray technique is a powerful biotechnological tool, expanding in a interesting way the vision with which issues in medicine are studied. Microarray technology, allows simultaneous evaluation of the expression of thousands of genes in different tissues of a given organism, and in different stages of development or environmental conditions. However, experiments with microarrays are still substantially costly and laborious, and as a consequence, they are usually conducted with relatively small sample sizes, thereby requiring a careful experimental design and statistical analysis. This paper adopts some applications of microarrays in risk analysis using R statistical software.
- Distribution function for the ratio of two normal random variablesPublication . Oliveira, Amilcar; Oliveira, Teresa; Seijas-Macias, J. AntonioThe 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 unimodal, 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.
- Modeling non-life insurance price for risk without historical informationPublication . Azevedo, Filipe Charters de; Oliveira, Teresa A.; Oliveira, AmilcarHow should an insurer price a risk for which there is no history? This work intends to show, step by step, which main mechanisms are needed to capture the tariff model of another insurance company minimizing the risk involved. The document generally deals with the price-making mechanisms in non-life insurance through the GLM regression models — Generalized Linear Model, more precisely the Poisson, Gamma and Tweedie models. Given the complexity of the application of these models in experimental design, it is studied a simpler way to characterize the rate, namely considering the Box–Cox transformation with SUR — Seemingly Unrelated Regression. An orthogonal experimental design to collect information is also presented as well as an application of these methods in the motor industry considering different companies.
- Item response theory : a first approachPublication . Nunes, Sandra; Oliveira, Teresa; Oliveira, AmilcarThe 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.