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The Weibull distribution is a versatile probability distribution widely applied in modeling the failure times of objects or systems. Its behavior is shaped by two essential parameters: the shape parameter and the scale parameter. By manipulating these parameters, the Weibull distribution adeptly captures diverse failure patterns observed in real-world scenarios. This flexibility and broad applicability make it an indispensable tool in reliability analysis and survival modeling. This manuscript explores five parameterizations of the Weibull distribution, each based on different moments, like mean, quantile, and mode. It meticulously characterizes each parameterization, introducing a novel one based on the model’s mode, along with its hazard and survival functions, shedding light on their unique properties. Additionally, it delves into the interpretation of regression coefficients when incorporating regression structures into these parameterizations. It is analytically established that all five parameterizations define the same log-likelihood function, underlining their equivalence. Through Monte Carlo simulation studies, the performances of these parameterizations are evaluated in terms of parameter estimations and residuals. The models are further applied to real-world data, illustrating their effectiveness in analyzing material fatigue life and survival data. In summary, this manuscript provides a comprehensive exploration of the Weibull distribution and its various parameterizations. It offers valuable insights into their applications and implications in modeling failure times, with potential contributions to diverse fields requiring reliability and survival analysis.

Many phenomena can be described by random variables that follow asymmetrical distributions. In the context of regression, when the response variable Y follows such a distribution, it is preferable to estimate the response variable for predictor values using the conditional median. Quantile regression models can be employed for this purpose. However, traditional models do not incorporate a distributional assumption for the response variable. To introduce a distributional assumption while preserving model flexibility, we propose new varying-coefficients quantile regression models based on the family of log-symmetric distributions. We achieve this by reparametrizing the distribution of the response variable using quantiles. Parameter estimation is performed using a maximum likelihood penalized method, and a back-fitting algorithm is developed. Additionally, we propose diagnostic techniques to identify potentially influential local observations and leverage points. Finally, we apply and illustrate the methodology using real pollution data from Padre Las Casas city, one of the most polluted cities in Latin America and the Caribbean according to the World Air Quality Index Ranking.

Income modeling is crucial in determining workers’ earnings and is an important research topic in labor economics. Traditional regressions based on normal distributions are statistical models widely applied. However, income data have an asymmetric behavior and are best modeled by non-normal distributions. The objective of this work is to propose parametric quantile regressions based on two asymmetric income distributions: Dagum and Singh–Maddala. The proposed quantile regression models are based on reparameterizations of the original distributions by inserting a quantile parameter. We present the reparameterizations, properties of the distributions, and the quantile regression models with their inferential aspects. We proceed with Monte Carlo simulation studies, considering the performance evaluation of the maximum likelihood estimation and an analysis of the empirical distribution of two types of residuals. The Monte Carlo results show that both models meet the expected outcomes. We apply the proposed quantile regression models to a household income data set provided by the National Institute of Statistics of Chile. We show that both proposed models have good performance in model fitting. Thus, we conclude that the obtained results favor the Singh–Maddala and Dagum quantile regression models for positive asymmetrically distributed data related to incomes. The economic implications of our investigation are discussed in the final section. Hence, our proposal can be a valuable addition to the tool-kit of applied statisticians and econometricians.

The increase in air pollution levels in recent decades around the world has caused a negative impact on human health. A recent investigation by the World Health Organization indicates that nine out of ten people on the planet breathe air containing high levels of pollutants and seven million people die each year from this cause. This problem is present in several cities in South America due to dangerous levels of particulate matter present in the air, particularly in the winter period, making it a public health problem. Santiago in Chile and Lima in Peru are among the ten cities with the highest levels of air pollution in South America. The location, climate, and anthropogenic conditions of these cities generate critical episodes of air pollution, especially in the coldest months. In this context, we developed a semiparametric model to predict particulate matter levels as a function of meteorological variables. For this, we discuss estimation and diagnostic procedures using a Student’s t-based partially varying coefficient model. Parameter estimation is performed through the penalized maximum likelihood method using smoothing splines. To obtain the parameter estimates, we present a weighted back-fitting algorithm implemented in R-project and Matlab software. In addition, we developed local influence techniques that allowed us to evaluate the potential influence of certain observations in the model using four different perturbation schemes. Finally, we applied the developed model to real data on air pollution and meteorological variables in Santiago and Lima.

In this paper, we study a semiparametric additive beta regression model using a parameterization based on the mean and a dispersion parameter. This model is useful for situations where the response variable is continuous and restricted to the unit interval, in addition to being related to other variables through a semiparametric regression structure. First, we formulate the model and then estimation of its parameters is discussed. A back-fitting algorithm is derived to attain the maximum penalized likelihood estimates by using natural cubic smoothing splines. We provide closed-form expressions for the score function, Fisher information matrix and its inverse. Local influence methods are derived as diagnostic tools. Finally, a practical illustration based on real data is presented and discussed.

Resumen El presente trabajo tiene por objeto indagar sobre los procesos de integración transfronterizos y el rol que en ellos juega la planificación territorial. Se observó que los esfuerzos integracionistas, ya sea, en procesos macro regionales o, en programas micro nacionales, no alcanzan la eficiencia ni eficacia deseada y la planificación urbanística, no juega un rol protagonista en ellos. Haciendo uso de una metodología cualitativa, el estudio fue circunscrito a Chile, comenzando por una contextualización histórica y actual de las fronteras del país, una revisión del tratamiento normativo y de las políticas de integración transfronteriza en las que participa el Estado, a nivel regional (UNASUR) y a nivel nacional, mediante los Comités de Integración Fronteriza. Posteriormente, se efectúa un análisis comparativo con procesos internacionales de integración transnacional, para luego, hacer una evaluación DAFO de los mismos, extrayéndose un listado de buenas y malas prácticas. Finalmente, se analiza un caso de estudio, que comprende la zona norte de Chile y Argentina, el cual permite corroborar la hipótesis y observar sobre la infrautilización del planeamiento territorial en materia de integración transfronteriza. Se concluye con una propuesta, en la que esta disciplina adquiere un rol más preponderante en los procesos de integración existentes. Abstract The present paper has the objective to inquire about the processes of cross - border integration and the role of territorial planning has in them. It was observed that the integrationist efforts, either in macro regional processes or in micro-national programs, do not reach the desired efficiency and effectiveness and urban planning, does not play a leading role in them. Using a qualitative methodology, the study was circumscribed to Chile, starting with a historical and current contextualization of the country's borders, a review of the normative treatment and integration policies in which the State participates, at the regional level (UNASUR) and at the national level, through the Border Integration Committees. Subsequently, a comparative analysis is carried out with international processes of transnational integration, then, to make a SWOT evaluation of the same, extracting a list of positives and negatives practices. Finally, a case study, which includes the northern Chilean and Argentinean areas, is analyzed, which allows the corroboration of the hypothesis and concluding with the underutilization of territorial planning in the area of cross - border integration. It concludes with a proposal, in which this discipline acquires a more preponderant role in the existing integration processes.

One of the main environmental problems that affects people’s health and quality of life is air pollution by particulate matter. Chile has nine of the ten most polluted cities in South America according to a report presented in 2019 by Greenpeace and AirVisual that measured the air quality index based on the levels of fine particles. Most Chilean cities are highly contaminated by particulate matter, especially during the months of April to August (the critical episode management period). The objective of this study is to predict particulate matter levels based on meteorological and climatic features, such as temperature, wind speed, wind direction, precipitation and relative air humidity in Talca, Chile, during the critical episode management periods between 2014 and 2018. Predictive models based on machine learning techniques were used, considering training datasets with meteorological and climatic data, and particulate matter levels from the three air quality monitoring stations in Talca, Chile. We carried out the training of 24 models to predict particulate matter levels considering the 24-h average and average between 05:00 to 11:00 p.m. For the model testing, data from the year 2018 during the critical episode management period were used. The obtained results indicate that our models are able to effectively predict levels of particulate matter, enabling correct management of critical episodes, especially for alert, pre-emergency and emergency conditions. We used the cross-platform and open-source programming language Python for the development and implementation of the proposed models and R-project for some visualizations.

Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.

Data mining is employed to extract useful information and to detect patterns from often large data sets, closely related to knowledge discovery in databases and data science. In this investigation, we formulate models based on machine learning algorithms to extract relevant information predicting student retention at various levels, using higher education data and specifying the relevant variables involved in the modeling. Then, we utilize this information to help the process of knowledge discovery. We predict student retention at each of three levels during their first, second, and third years of study, obtaining models with an accuracy that exceeds 80% in all scenarios. These models allow us to adequately predict the level when dropout occurs. Among the machine learning algorithms used in this work are: decision trees, k-nearest neighbors, logistic regression, naive Bayes, random forest, and support vector machines, of which the random forest technique performs the best. We detect that secondary educational score and the community poverty index are important predictive variables, which have not been previously reported in educational studies of this type. The dropout assessment at various levels reported here is valid for higher education institutions around the world with similar conditions to the Chilean case, where dropout rates affect the efficiency of such institutions. Having the ability to predict dropout based on student’s data enables these institutions to take preventative measures, avoiding the dropouts. In the case study, balancing the majority and minority classes improves the performance of the algorithms.

Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM.

We propose a methodology useful for food services, allowing contribution margins to be optimized. This is based on statistical tools, inventory models and financial indicators. To reduce the gap between theory and practice, we apply this methodology to the case study of a Chilean company to show its potential. We conduct a real-world demand data analysis for perishable and non-perishable products in the companys inventory assortment. Then, we use suitable inventory models to optimize the associated costs. We compare the proposed optimized system with the non-optimized system currently employed by the company, using financial indicators.

Mortality processes and the distribution of the diameter at breast height (DBH) of trees are two important problems in forestry. Trees die due to several factors caused by stress according to a phenomenon similar to material fatigue. Specifically, the force (rate) of mortality of trees quickly increases at a first stage and then reaches a maximum. In that moment, this rate slowly decreases until stabilizing at a constant value in the long term establishing a second stage of such a rate. Birnbaum-Saunders (BS) distributions are models that have received considerable attention currently due to their interesting properties. BS models have their genesis from a problem of material fatigue and present a failure or hazard rate (equivalent to the force of mortality) that has the same behavior as that of the DBH of trees. Then, BS distributions have arguments that transform them into models that can be useful in forestry. In this paper, we present a methodology based on BS distributions associated with this forest thematic. To complete this study, we perform an application of five real DBH data sets (some of them unpublished) that provides statistical evidence in favor of the BS methodology in relation to the forestry standard methodology. This application provides valuable financial information that can be used for making decisions in forestry.Los procesos de mortalidad y la distribución del diámetro a la altura del pecho (DAP) de árboles son dos problemas importantes en el área forestal. Los árboles mueren debido a diversos factores causados por estrés mediante un fenómeno similar a la fatiga de materiales. Específicamente, la fuerza (tasa) de mortalidad de árboles crece rápidamente en una primera fase y luego alcanza un máximo, momento en el que comienza una segunda fase en donde esta tasa decrece lentamente estabilizándose en una constante en el largo plazo. Distribuciones Birnbaum-Saunders (BS) son modelos que han recibido una atención considerable en la actualidad debido a sus interesantes propiedades. Modelos BS nacen de un problema de fatiga de materiales y poseen una tasa de fallas (equivalente a la fuerza de mortalidad) que se comporta de la misma forma que ésa del DAP de árboles. Entonces, distribuciones BS poseen argumentos que las transforman en modelos que puede ser útiles en las ciencias forestales. En este trabajo, presentamos una metodología basada en la distribución BS asociada con esta temática forestal. Para finalizar, realizamos una aplicación con cinco conjuntos de datos reales (algunos de ellos no publicados) de DAP que proporciona una evidencia estadística en favor de la metodología BS en relación a la metodología estándar usada en ciencias forestales. Esta aplicación entrega información que puede ser valiosa para tomar decisiones forestales.

Since its origins and numerous applications in material science, the Birnbaum–Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum–Saunders and log-Birnbaum–Saunders distributions in univariate and multivariate versions. There are now well-developed methods for estimation and diagnostics that allow in-depth analyses. This paper gives a detailed review of existing methods and of relevant literature, introducing properties and theoretical results in a systematic way. To emphasise the range of suitable applications, full analyses are included of examples based on regression and diagnostics in material science, spatial data modelling in agricultural engineering and control charts for environmental monitoring. However, potential future uses in new areas such as business, economics, finance and insurance are also discussed. This work is presented to provide a full tool-kit of novel statistical models and methods to encourage other researchers to implement them in these new areas. It is expected that the methods will have the same positive impact in the new areas as they have had elsewhere.