PPGMAE - Mestrado em Matemática Aplicada e Estatística
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Master Thesis Análise de modelos de regressão para taxas estaduais de mortalidade por Covid-19 no Brasil(Universidade Federal do Rio Grande do Norte, 2025-05-20) Vieira, Mirela da Silva; Lemonte, Artur José; https://orcid.org/0000-0002-0249-7474; http://lattes.cnpq.br/4283549028869521; http://lattes.cnpq.br/5028431925410574; Costa, Eliardo Guimarães da; http://lattes.cnpq.br/3160805152538713; Magalhães, Tiago Maia; https://orcid.org/0000-0003-3814-9532; http://lattes.cnpq.br/7953363504273397Master Thesis Inferência bayesiana para modelos binomiais com priori conjugada baseada em generalizações da distribuição beta(Universidade Federal do Rio Grande do Norte, 2025-03-20) Leite, Luana Mayara Lucas; Pereira, Marcelo Bourguignon; https://orcid.org/0000-0002-1182-5193; http://lattes.cnpq.br/9358366674842900; http://lattes.cnpq.br/0862072928793748; Costa, Eliardo Guimarães da; Costa, José Mir Justino daThe present dissertation aims to propose alternative conjugate prior distributions for the binomial model based on generalizations of the beta distribution. In this context, the developed methodology seeks to estimate the proportion parameter π of the binomial distribution using a Bayesian approach, employing generalizations of the beta distribution as priors in such a way that the posterior distribution also belongs to the same class as the prior. Additionally, the properties of these distributions will be studied in detail, with simulations conducted through random number generation. Their advantages over the beta distribution will be assessed, as the aim is to achieve better fitting results than those obtained by the beta distribution when compared.Master Thesis Inferência bayesiana para modelos Poisson com priori conjugada baseada em misturas da distribuição Gama(Universidade Federal do Rio Grande do Norte, 2025-03-17) Araújo, Karine dos Santos; Pereira, Marcelo Bourguignon; https://orcid.org/0000-0002-1182-5193; http://lattes.cnpq.br/9358366674842900; http://lattes.cnpq.br/8535082485035743; Nascimento, Fernando Ferraz do; Souza Filho, Nelson Lima deBayesian inference is a statistical methodology that combines prior information about model parameters with observational data to estimate the posterior distribution of unknown parameters. One of the advantages of using conjugate priors is that the resulting posterior distribution remains within the same family of distributions as the prior, which facilitates both the calculations and the intuitive interpretation of the posterior parameters. In this study, we adopted mixtures of Gamma distributions as conjugate priors for the λ parameter of the Poisson distribution, which provides a more flexible approach capable of better adjusting to different data characteristics. The mixtures of Gamma distributions explored in this work include the generalized Lindley distribution 1 (ABOUAMMOH; ALSHANGITI; RAGAB, 2015), the generalized Lindley distribution 2 (RAMOS; LOUZADA; MOALA, 2021) and the generalized Lindley distribution 3 (ZAKERZADEH; DOLATI, 2009). These distributions are extensions of the classic Lindley distribution. To illustrate the practical application of the proposed methodology, we carried out a study with real data.Master Thesis Modelando eventos extremos de precipitação no semiárido nordestino utilizando a Distribuição ZIGEV(Universidade Federal do Rio Grande do Norte, 2025-02-21) Araújo, Iarythssa Duarte de; Medeiros, Francisco Moisés Cândido de; https://orcid.org/0000-0001-6751-2666; http://lattes.cnpq.br/2662558366496381; http://lattes.cnpq.br/7633642310017371; Rodrigues, Daniele Tôrres; Costa, Eliardo Guimarães da; Morales, Fidel Ernesto CastroThe semiárido region of Northeast Brazil (NEB) is characterized by irregular rainfall patterns and high evapotranspiration rates, leading to water scarcity. Additionally, the region is prone to extreme precipitation events, which can trigger socio-environmental disasters with severe impacts. Despite the development of various models for modeling extreme events, their application in the semi-arid region of the NEB is limited by the lack of detailed data and methodologies tailored to its local characteristics. This study aims to model extreme precipitation events in this region using the Zero-Inflated Generalized Extreme Value (ZIGEV) distribution. The methodological approach is based on Bayesian inference, which incorporates uncertainties and prior information into the parameter estimation process. The analysis focuses on a sub-region of the NEB semi-arid zone, marked by extremely low annual precipitation and high susceptibility to extreme precipitation events. Daily precipitation data from 16 (sixteen) localities within the study area were used to fit the model and estimate the return levels of extreme events. The results demonstrated the effectiveness of the ZIGEV model in predicting extreme precipitation events, providing reliable parameter estimates and outperforming the standard GEV model, which faced convergence issues in many datasets. The ZIGEV model proved suitable for data with a high proportion of zeros and also converged to the GEV model when the proportion of zeros was lower. Additionally, the estimated return levels for each locality provided valuable insights into the occurrence and intensity patterns of these events, contributing to water resource management and the development of disaster mitigation strategies for the NEB semi-arid region.Master Thesis Existência de soluções para uma classe de equações de Kirchhoff-Schrödinger com crescimento crítico de Sobolev(Universidade Federal do Rio Grande do Norte, 2025-02-14) Silva, Cristiano Victor Medeiros da; Souza, Diego Ferraz de; http://lattes.cnpq.br/4757061859245287; http://lattes.cnpq.br/0991482396568693; Silva, Esteban Pereira da; Duarte, Ronaldo Cesar; Parra, Juan Luis Miguel Arratia; López, Pedro Eduardo Ubilla; Clemente, Rodrigo GenuinoIn this work, we establish the existence of positive solutions for a class of stationary Kirchhoff-Schrödinger equations defined in the whole R3 with nonlinearity with critical growth in the Sobolev sense and nonnegative potential that can decay to zero at infinity. For this purpose, we use the variational method of critical point theory, which consists of associating the solutions of the equation to the critical points of a suitable functional. Furthermore, the nonlinearity is general and does not satisfy the well-known AmbrosettiRabinowitz condition, which makes the study of the compactness associated with the problem and the boundedness of Palais-Smale sequences more sophisticated. In this context, the main tools used to achieve our main results were the use of the mountain pass theorem and the Lions’ compactness principle, in addition to the common basis which consists of basic results of measure theory and Lebesgue integration, functional analysis and nonlinear functional analysis.Master Thesis Modelagem matemática e computacional do processo de reinjeção de água produzida em reservatórios de petróleo(Universidade Federal do Rio Grande do Norte, 2025-02-26) Assunção, Brunna Karla de Morais Souza; Lima, Sidarta Araújo de; http://lattes.cnpq.br/7285935215651168; http://lattes.cnpq.br/6826569527056669; Santos, Adriano dos; Fernando, Honório Joaquim; Radtke, Luiz CarlosProduced water reinjection is a process used in oil reservoirs, consisting of reinjecting the water produced during oil production. However, this technique can be a!ected by reactive phenomena such as adsorption and mechanical retention. These phenomena may cause formation damage, leading to injectivity loss and, consequently, negatively impacting oil production curves. Given this, it is essential to develop mathematical and computational models that accurately describe the processes governing particle injection in porous media. In this context, the mathematical modeling developed in this dissertation aims to derive a system of partial di!erential equations that govern the hydrodynamics and particle transport in an oil reservoir. The hydrodynamics are governed by the total mass balance of the fluid phases, along with the total Darcy’s law, while particle transport is described by the advective-dispersive-reactive transport equation. The reactive nature of particle transport is modeled using kinetic laws expressed through ordinary di!erential equations. Regarding computational modeling, the hydrodynamics are discretized using the dual mixed finite element method, while the movement of the fluid phases is approximated using the explicit Central-Upwind finite volume method. For the discretization of the particle transport equation, we employ a predictor-corrector algorithm, which, due to the nature of the di!usive term, allows the equation to be numerically solved using the two aforementioned methods. The implemented computational simulator was validated against analytical solutions to assess its accuracy. The obtained numerical results demonstrate that the simulator can accurately and stably quantify the produced water reinjection process in oil reservoirs. Finally, the computational model is applied to a more realistic scenario, considering a quarter of a five-spot domain.Master Thesis Involuções da álgebra de Grassmann: um estudo sobre *- polinômios centrais, *-identidades e *-isomorfismos(Universidade Federal do Rio Grande do Norte, 2025-01-24) Santos, Lígia Danielly Rocha dos; Guimarães, Alan de Araújo; http://lattes.cnpq.br/6286902372305694; http://lattes.cnpq.br/8469906596468208; Kuzmin, Alexey; Tsurkov, Arkady; Macêdo, David Levi da Silva; Silva, Diogo Diniz Pereira da Silva e; Teixeira, José Victor Gomes; Araújo, Laise Dias Alves; Morais, Pedro Henrique Martins De; 01987809580Let K be a field of characteristic distinct from two, E be the Grassmann algebra of a K-vector space with infinite and countable base L and let φ be any involution. Based on the article (CENTRONE; GONCALVES; SILVA, 2020), we present generating sets for the ∗-polynomial identities and ∗-central polynomials of the Grassmann algebra, with a strong distinction between the cases char(K) = 0 and char(K) > 2. According to (DINIZ; GUIMARÃES; ROCHA, 2024), when φ satisfies certain conditions, we show that there is homogeneous involution φl (i.e., φl(L) = L) such that (E, φ) and (E, φl) are ∗-isomorphic. Additionally, we present certain necessary and sufficient condition for two homogeneous involutions to produce ∗-isomorphic structures. As a consequence, we obtain examples of algebras that are ∗-PI-equivalent and that are not ∗-isomorphic algebras.Master Thesis Modelos espaciais e espaço-temporais para contagem de chuvas extremas na costa leste do Nordeste do Brasil(Universidade Federal do Rio Grande do Norte, 2025-01-10) Luz, Josiel Oliveira da; Morales, Fidel Ernesto Castro; http://lattes.cnpq.br/8552159154343151; https://orcid.org/0000-0001-6128-9432; http://lattes.cnpq.br/6106700517329582; Costa, Eliardo Guimarães da; http://lattes.cnpq.br/3160805152538713; Cabral Júnior, Jorio BezerraThe study of climatic extremes is essential for understanding the occurrence of natural disasters. It becomes even more important when the tools available for this analysis do not perform their functions accurately. This is the case with the extreme rainfall events that occur on the east coast of north-eastern Brazil, where estimates from the Tropical Rainfall Measuring Mission satellite (TRMM) and the Tropical Rainfall Measuring Mission satellite (TRMM) are not accurate. (TRMM) satellite and the Global Precipitation Measurement (GPM) satellite tend to underestimate extreme precipitation. This study therefore set out to analyse the performance of spatial and spatio-temporal models, available in the literature and implemented in the R language, when applied to extreme rainfall count data from the east coast of the Northeast, as well as comparing the performance of the models with the performance of the satellite for the study context. The aim is to build up the knowledge needed to support the development of mitigation measures for natural disasters. To this end, the study variable was the number of times the daily rainfall accumulated exceeded or was equal to the threshold of 30 millimetres over the course of a year, so that the counts were made per rainfall station. This variable is one of the 27 indices adopted by the World Meteorological Organisation (WMO) to study climate variations. The time series studied has records of daily rainfall accumulations from 36 stations during the period from 1991 to 2022. In addition to precipitation, it contains the latitude, longitude and altitude of the stations. The data was taken from the National Meteorological Institute (INMET) and the National Water and Sanitation Agency (ANA). With regard to the methodology adopted for the main parts of the study, the research began with a literature search for R language packages that worked with count data from a spatial and spatio-temporal perspective. After the search and before using the models, a descriptive analysis of the data was carried out, in which the means, medians, standard deviations, coefficients of variation and amplitudes by year and season were calculated. The investigation continued by analysing the study variable and the covariates latitude, longitude and altitude using scatter plots. Spatial and temporal dependencies were also analysed using variograms. Once the descriptive analysis had been completed, the cross-validation methodology was used to assess the performance of the models. The comparison between the models and the satellite data was made using mean square error, bias and correlation coefficient statistics. The results achieved in this research are encouraging. Extremes occur more frequently in regions close to the coast, with spatial dependence and temporal dependence for only a few stations. Furthermore, in a purely observational analysis, there is an indication of patterns of extremes repeating every 10 years from 1991 onwards. It was also possible to see that satellite data underestimates the extremes in the region studied, especially in the south of the area. Four packages implemented in the R language capable of working with the study data were identified in the literature, and six models from these packages were adjusted. The models obtained excellent results when compared to the satellite estimates. They proved to be better in most of the locations tested. They also show that they have great potential for generating more reliable data for analysing precipitation extremes.Master Thesis Avaliação do desempenho do gráfico de controle de Shewhart para o processo OIB-INAR(1) e comparação com o desempenho do gráfico de Shewhart do processo Borel INAR(1)(Universidade Federal do Rio Grande do Norte, 2024-09-13) Ferreira, Camiliane Azevedo; Pinho, André Luís Santos de; https://orcid.org/0000-0002-2975-4637; http://lattes.cnpq.br/7753762932186347; https://orcid.org/0000-0002-3268-991X; http://lattes.cnpq.br/0542984976258690; Souza, Isaac Jales Costa; Sales, Lucas de Oliveira Ferreira de; Fernandez, Luz Milena ZeaIn the face of technological advances and the large amount of information generated, count data is becoming increasingly autocorrelated. This creates a growing need for new models and monitoring tools that take into account the specific characteristics of this data. In this paper, we propose a Shewhart control chart for autocorrelated count data that can be modeled by an INAR(1) process with innovations from the inflated Borel distribution of ones (OIB-INAR(1)). This model is well-suited for modeling data with an inflation of ones, as well as underdispesion, equidispersion, or overdispersion. Addicionally, we will compare the performance of this control chart with that of a Borel INAR(1) process, which models series of counts truncated at zero that show underdispersion, equidispersion or overdispersion. The Borel INAR(1) process can be seen as a particular case of the OIB-INAR(1) process. The performance evaluation of the proposed approach is based on the average number of samples required to detect an alarm (NMAF and NMA) in different scenarios. The determination of the upper control limit (UCL) and the evaluation of the performance of the graphs are carried out by means of computational studies using Monte Carlo simulations. To illustrate the applicability of the proposed method, we present an example with real data.Master Thesis A distribuição Borel inflacionada de uns e um processo autoregressivo de primeira ordem para valores inteiros com inovações Borel inflacionada de uns(Universidade Federal do Rio Grande do Norte, 2024-02-02) Ciriaco, Beatriz Ariadna da Silva; Pinho, André Luís Santos de; Fernandez, Luz Milena Zea; https://orcid.org/0000-0001-8335-9446; http://lattes.cnpq.br/0576675498537949; https://orcid.org/0000-0002-2975-4637; http://lattes.cnpq.br/7753762932186347; http://lattes.cnpq.br/3864348097536219; Nascimento, Antônio Marcos Batista do; Souza, Isaac Jales CostaAs time series of integer values are based on counts, such as the autoregressive processes of integer values (INAR), they may contain an excessive number of repeated values that could harm the inferential analysis if this behavior is not known. Then it becomes necessary to understand time series inflated models for integer values. Some models have been developed to study zero-inflated data, however, this work focuses on the one-inflated model (OI) and the autoregressive process with one-inflated innovations (OI-INAR(1)). Thus, the Oneinflated Borel (OIB) model and the INAR(1) process with one-inflated Borel innovations (OIB-INAR(1)) are proposed. In this work the properties, such as expectation, variance, dispersion index and probability generating function, of these models are developed, as well as the methods for estimating the parameters of the OIB model, such as the method of moments and maximum likelihood. Likewise, for the OIB-INAR(1) process, the conditional least squares and conditional maximum likelihood methods, in addition to one-step-ahead prediction methodologies are studied. Finally, an application is made adjusting the OIBINAR(1) model.Master Thesis Aprimoramento do teste da razão de verossimilhanças em modelos de regressão beta-prime(Universidade Federal do Rio Grande do Norte, 2024-03-26) Silva Júnior, Ivonaldo Silvestre da; Medeiros, Francisco Moisés Cândido de; https://orcid.org/0000-0001-6751-2666; http://lattes.cnpq.br/2662558366496381; http://lattes.cnpq.br/3715292067744966; Magalhães, Tiago Maia; Lemonte, Artur JoséThis paper deals with the issue of testing hypotheses in beta-prime regression models in small and moderate-sized samples. We focus on the likelihood ratio test, which is unreliable when the sample size is not large enough to guarantee a good approximation between the exact distribution of the test statistic and the corresponding chi-squared asymptotic distribution. Bartlett, Skovgaard and Bartlett-bootstrap corrections typically attenuate the size distortion of the test. Here, we derive a Bartlett correction and a Skovgaard adjustment for the likelihood ratio test on beta-prime regression models. We numerically compare the usual, corrected and bootstrapped tests, through simulations. Our results suggest that the corrected and bootstrapped tests exhibit type I probability error closer to the chosen nominal level. The analytically corrected tests perform with the advantage of not requiring computationally intensive calculations. We present a real data application to illustrate the usefulness of the modified tests.Master Thesis Modelos de regressão GJS longitudinais(Universidade Federal do Rio Grande do Norte, 2024-03-21) Santos, Paulo César dos; Lemonte, Artur José; https://orcid.org/0000-0002-0249-7474; http://lattes.cnpq.br/4283549028869521; https://orcid.org/0000-0001-7391-0337; http://lattes.cnpq.br/2069898808096779; Queiroz, Francisco Felipe de; Fernandez, Luz Milena Zea; https://orcid.org/0000-0001-8335-9446; http://lattes.cnpq.br/0576675498537949Weextend the class of GJS regression models that model continuous variables with support in the interval (0,1) to the case of correlated data, such as those coming from repeated measures, longitudinal or grouped data studies. The extension was carried out using the generalized linear mixed model methodology and parameter estimates are obtained based on the maximum likelihood (MV) method. The computational implementation combines the Gauss-Hermite quadrature to obtain the marginal density of the response variable and the BFGS non-linear optimization algorithm, implemented in the optim function of the computational software R. Monte Carlo simulations were performed to verify the performance of the MV estimators of the model parameters in samples of finite size. The simulation results suggest that the MV approach provides estimators with good properties. Additionally, we propose the randomized quantile residual to ascertain the quality of the f it. Furthermore, the effectiveness of the proposed residue in detecting some forms of model inadequacy was verified. Finally, we illustrate the methodology developed by applying it to a set of real data.Master Thesis Integração numérica para funções compostas em domínios multidimensionais através de uma quadratura de Lebesgue(Universidade Federal do Rio Grande do Norte, 2024-03-12) Guanabara, Lucas Matheus Augusto Olimpio; Costa, Eliardo Guimarães da; Solheid, Bruno dos Santos; http://lattes.cnpq.br/3160805152538713; http://lattes.cnpq.br/3695975538646224; Sassi, Gilberto Pereira; Souza, Diego Ferraz deThe present dissertation aims to introduce a numerical integration method, whose application will run on domains containing a high number of dimensions. In this regard, the developed methodology seeks to present a Lebesgue quadrature, which is based on partitions of the image of a function, where each weight is associated with a value of the function defined in its image. For Riemann-Integrable functions, we demonstrate the existence of a Lebesgue quadrature and show how to construct quadratures of this type for composite functions, in which the method exhibited good efficiency, surpassing quasi-Monte Carlo methods. The method involves arbitrarily approximating the value of a given finite sum using information generated by a histogram, to demonstrate that the numerical integration of a composite function, whose argument’s density has been previously determined, can be evaluated very easily.Master Thesis Análise espaço-temporal da frequência de homicídios nos bairros de Natal-RN no período de 2011 a 2021(Universidade Federal do Rio Grande do Norte, 2023-11-22) Ribeiro, Matheus Wingles Alves; Morales, Fidel Ernesto Castro; Campos, Járvis; http://lattes.cnpq.br/8552159154343151; https://orcid.org/0000-0002-9561-1693; http://lattes.cnpq.br/7172006162024828; Costa, Eliardo Guimarães da; http://orcid.org/0000-0003-4528-0379; http://lattes.cnpq.br/3160805152538713; Rodrigues, Francisco Alixandre ÁvilaIn this dissertation, a retrospective study is conducted on the number of Intentional Lethal Violent Crimes in the neighborhoods of Natal from 2011 to 2021. Specifically, it investigates whether there is a causal relationship between the number of intentional homicides and a series of factors, such as demographic, socioeconomic, geographical location, and infrastructure investment characteristics in the neighborhoods. Additionally, it examines whether the year 2020, during which mobility restrictions were imposed in the city, influenced the occurrence of homicides, as well as whether there were significant dierences in the frequency of this event according to the dierent administrations of the state of Rio Grande do Norte that occurred during the study period. The statistical method used to test the research hypotheses is the space-time model for area data, which is structured with Conditional Autoregressive Priors of the space-time components. This model uses the Bayesian paradigm, and the estimation of its parameters is carried out through the Markov Chain Monte Carlo method. It was found that factors such as Average Nominal Income, Illiteracy rate, Population Density, and the number of Enterprises in the region were significant for the increase in these crimes. It was also observed that, during the analysis of the state government administrations over the study period, the last administration had a positive impact on the reduction of homicides. Furthermore, in comparison with the North Zone, both the East Zone and the South Zone recorded a significant reduction in homicide rates, unlike what was observed in the West Zone.Master Thesis Z2-graduações da álgebra de Grassmann: construção, PI-equivalência e isomorfismos(Universidade Federal do Rio Grande do Norte, 2023-08-30) Silva, Ana Beatriz Gomes da; Guimarães, Alan de Araújo; http://lattes.cnpq.br/6286902372305694; http://lattes.cnpq.br/8666377050998073; Bezerra Júnior, Claudemir Fideles; Pimentel, Elaine Gouvea; https://orcid.org/0000-0002-7113-0801; http://lattes.cnpq.br/3298246411086415; Centrone, LúcioThe focus of our dissertation is to develope a study on the Z2-gradings of the infinitedimensional Grassmann algebra E. The homogeneous Z2-gradings and their Z2-graded identities are already well known in the literature, see (VINCENZO; SILVA, 2009), (CENTRONE, 2011) e (GONÇALVES, 2018). Nevertheless, the construction of nonhomogeneous Z2-gradings demands the use of the duality between these structures and automorphisms of order ≤ 2 acting on E. Through this, we will study the non-homogeneous Z2-gradings, producing results on their construction. Next, we will investigate under what conditions a non-homogeneous Z2-grading is isomorphic to the canonical Z2-grading of E. Finally, we will provide a Z2-grading on E in which there is no non-zero element of the space L homogeneous, giving a negative answer to the conjecture presented in (GUIMARÃES; KOSHLUKOV, 2023).Master Thesis Um guia para planejamento e análise de experimentos na área educacional(Universidade Federal do Rio Grande do Norte, 2023-06-27) Apolinario, Carla de Moraes; Vivacqua, Carla Almeida; https://orcid.org/0000-0002-4058-8289; http://lattes.cnpq.br/4339735174795014; http://lattes.cnpq.br/2572084930383095; Pinho, Andre Luis Santos de; https://orcid.org/0000-0002-2975-4637; http://lattes.cnpq.br/7753762932186347; Weissheimer, Janaina; https://orcid.org/0000-0002-6318-4906; http://lattes.cnpq.br/7345837860360864; Araujo, Andre Luis Calado; http://lattes.cnpq.br/7133712883742750Education in Brazil has been presenting challenges challenges of various kinds. During the 20th century the main educational challenge was access to schools and combating the high rate of illiteracy. The construction of public schools as a way of facilitating access to basic education led to other challenges that persist to the present day, such as the low quality of the education offered, a constant and relevant theme throughout the world, since the quality of education is a critical issue for the development of a country. Several studies have been carried out with the aim of identifying ways to improve teaching and learning and one way to identify best practices is to conduct a statistical experiment as a way to establish a causal relationship between different factors and students’ academic performance. Furthermore, these studies make it possible to evaluate the impact of public policies and government programs aimed at improving education, helping to direct resources more efficiently and effectively. As important as performing these interventions is conducting them properly so that it is possible to obtain reliable data. With the wide variety of existing statistical techniques, it is common for researchers from other areas to innapropriately use of experimental statistics when conducting an intervention. In this work, a literature review is carried out as a way of mapping studies that use experimental statistics in the educational context, in order to identify the difficulties found by researchers, as well as good practices carried out, in addition to carrying a case study to identify possible practice difficulties that were not noted in the review. This work aims to disseminate the correct use of experimental statistics techniques in a clear, objective and understandable way for researchers from other areas who are not familiar with that subject. To achieve this goal, an accessible and simplified language is adopted when explaining complex concepts, using concrete examples and graphics that help to visualize the statistical concepts. Moreover, the importance of using controlled experiments and randomization are emphasized, which allow inferences followed up on the basis of quantitative evidence. Additionally, as part of the proposed work, a guide will be developed that will present the steps and important points to plan an experiment properly, guaranteeing the validity and reliability of the results obtained. This guide will include guidance on designing the experiment, choosing sample size, selecting experimental and control groups, randomization, selecting appropriate statistical tests, and other aspects crucial to successful experimental research. It is hoped that this guide will provide a useful reference for researchers from other fields who wish to use experimental statistics correctly and effectively in their researchMaster Thesis Uma nova abordagem topológica para métrica intervalar(Universidade Federal do Rio Grande do Norte, 2023-03-28) Silva, Jefferson Henrique da; Santana, Fagner Lemos de; http://lattes.cnpq.br/9444112594388983; http://lattes.cnpq.br/6930040968143313; Lima, Annaxsuel Araújo de; Bedregal, Benjamin Rene Callejas; http://lattes.cnpq.br/4601263005352005; Santiago, Regivan Hugo Nunes; Lima, Sidarta Araújo deMaster Thesis Resíduos no modelo de regressão Bell-Touchard(Universidade Federal do Rio Grande do Norte, 2023-04-20) Medeiros, Israel Costa Smith de; Lemonte, Artur José; https://orcid.org/0000-0002-0249-7474; http://lattes.cnpq.br/4283549028869521; http://lattes.cnpq.br/0875413781470256; Garay, Aldo William Medina; Morales, Fidel Ernesto Castro; http://lattes.cnpq.br/8552159154343151The Bell-Touchard distribution and its regression model, are a promising alternative to the statistical models that are already established in the count data modelling, as Poisson and Negative Binomial models. Count data are observations such that the variable assume non-negative integer values and are useful, for example, to modelling the number of claims that happened in a given period of time, which are of interest to insurance companies, for example. The Poisson model, for this purpose, is not a model that does work well with the overdispersion problem, situation in which the variance is greater than the expectation. Alternatives to deal with this kind of problem emerged, being proposed the zero-inĆated models and the Negative Binomial model. The Bell-Touchard model, that is a generalization of Bell model, is an recent alternative that try to solve this kind of problem. In this masterŠs dissertation, a deeper research is made about residuals in the Bell-Touchard regression model and the main goal is to improve the academic literature about count data.Master Thesis Segmentação de sequências em cadeias de Markov usando máxima verossimilhança penalizada(Universidade Federal do Rio Grande do Norte, 2023-03-27) Rodrigues, Franklin Diego de Lima; Medeiros, Francisco Moisés Cândido de; Castro, Bruno Monte de; https://orcid.org/0000-0001-6751-2666; http://lattes.cnpq.br/2662558366496381; http://lattes.cnpq.br/9469776083562927; Costa, Eliardo Guimarães da; http://orcid.org/0000-0003-4528-0379; http://lattes.cnpq.br/3160805152538713; Cerqueira, AndressaThe sequence segmentation problem aims to partition a sequence or a set of them into a finite number of distinct segments as homogeneous as possible. In this paper, we consider the problem of segmenting a set of random sequences, with values in a finite alphabet E, into a finite number of independent blocks. Under the assumption that the data follow a Markov chain, the problem consists in estimating the number and position of the change points in the sequence. For this, we propose the using of the penalized maximum likelihood criterion to infer, simultaneously, the number and position of the change points. The main result of our work is the demonstration of the theorem that guarantees the strong consistency of the set of change points estimators for a sufficiently large number of samples.Master Thesis Avaliação do desempenho e aplicação do gráfico de controle EWMA para o processo estocástico POMINAR(1)(Universidade Federal do Rio Grande do Norte, 2023-03-31) Santos, Edwin Castro Fernandes dos; Pinho, André Luis Santos de; https://orcid.org/0000-0002-2975-4637; http://lattes.cnpq.br/7753762932186347; http://lattes.cnpq.br/0368204181534984; Fernandez, Luz Milena Zea; https://orcid.org/0000-0001-8335-9446; http://lattes.cnpq.br/0576675498537949; Queiroz, Francisco Felipe deIn this work we propose to evaluate the performance of the EWMA control chart, adapting it to the first-order mixed autoregressive model with Poisson innovations, called POMINAR(1), which is composed of two operators known as thinning binomial and thinning Poisson. The objective is to compare the results obtained with those of the Shewhart control chart, and to show that the EWMA control chart is more efficient to detect deviations in the process mean below 1.5 standard deviation. For this, the EWMA control chart and its expectation are defined. Two theorems and two corollaries are proposed in order to define the variance according to the size of the rational subgroup. Moreover, the EWMA upper and lower control limits will be set, to analyze its performance. After that, an analysis will be made comparing the values found in a simulation using the EWMA control chart with the results obtained using the Shewhart control chart. Finally, two applications with real data using the EWMA control chart are presented. The first situation relates to the Criminal Data Section on the Forecasting Principles website. The chosen variable represents the number of monthly robberies reported in political district nº 12, in Pittsburgh (USA), from Jan/1990 to Dec/2001, with a total of 144 observations. The second situation is the count of different IP addresses recorded in a period of two minutes in duration on the server of the Department of Statistics of the University of Wüsrzburg, on November 29, 2005, between 10 a.m. and 6 p.m. with 241 observations.