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In reliability studies, we are interested in the behaviour of a system when it interacts with its surrounding environment. To assess the system’s behaviour in a reliability sense, we can take the system’s intrinsic quality as strength and the outcome of interactions as stress. Failure is observed whenever stress exceeds strength. Taking Y as a random variable representing the stress the system experiences and random variable X as its strength, the probability of not failing can be taken as a proxy for the reliability of the component and given as P(Y

In reliability contexts, probabilities of the type R=P(X

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.

Abstract This paper adapts Hamiltonian Monte Carlo methods for application in log-symmetric autoregressive conditional duration models. These recent models are based on a class of log-symmetric distributions. In this class, it is possible to model both median and skewness of the duration time distribution. We use the Bayesian approach to estimate the model parameters of some log-symmetric autoregressive conditional duration models and evaluate their performance using a Monte Carlo simulation study. The usefulness of the estimation methodology is demonstrated by analyzing a high frequency financial data set from the German DAX of 2016.

ABSTRACT Objective To investigate the potential role of the Vulnerable Elders Survey to identify older adults with limited life expectancy in primary healthcare settings. Method This cross-sectional study was performed in all (nine) healthcare units in Jatai, Goiás (Brazil) from July to December 2018. A sample size of 407 older adults was obtained considering an older population (≥ 60 years old). Participants answered a questionnaire about sociodemographic and clinical characteristics, including the Vulnerable Elders Survey and the Suemoto index. We tested the association between limited life expectancy and the Vulnerable Elders Survey using multiple logistic regression analysis. Results The mean age was 68.9 ± 6.6 yo, and 58.0% were women. The mean score of the Vulnerable Elders Survey was 2.0 ± 2.2, the mean score of Suemoto index was 31.5 ± 21.1%, and 17.2% had limited life expectancy. The Vulnerable Elders Survey was associated with limited life expectancy (OR = 1.57; p = < 0.0001). Conclusion The Vulnerable Elders Survey was able to identify older adults with limited life expectancy in primary healthcare settings and can play a role in detecting older adults who would not benefit from screening and strict control of chronic diseases.

ABSTRACT OBJECTIVE: To estimate the relation between catastrophic health expenditure (CHE) and multimorbidity in a national representative sample of the Brazilian population aged 50 year or older. METHODS: This study used data from 8,347 participants of the Estudo Longitudinal de Saúde dos Idosos Brasileiros (ELSI – Brazilian Longitudinal Study of Aging) conducted in 2015–2016. The dependent variable was CHE, defined by the ratio between the health expenses of the adult aged 50 years or older and the household income. The variable of interest was multimorbidity (two or more chronic diseases) and the variable used for stratification was the wealth score. The main analyses were based on multivariate logistic regression. RESULTS: The prevalence of CHE was 17.9% and 7.5%, for expenditures corresponding to 10 and 25% of the household income, respectively. The prevalence of multimorbidity was 63.2%. Multimorbidity showed positive and independent associations with CHE (OR = 1.95, 95%CI 1.67–2.28, and OR = 1.40, 95%CI 1.11–1.76 for expenditures corresponding to 10% and 25%, respectively). Expenditures associated with multimorbidity were higher among those with lower wealth scores. CONCLUSIONS: The results draw attention to the need for an integrated approach of multimorbidity in health services, in order to avoid CHE, particularly among older adults with worse socioeconomic conditions.

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.

Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum–Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum–Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.

This paper presents a method to perform a location recommendation based on multiple criteria allowing noised coordinates. More speciï¬ cally, the skyline query is adapted to handle those noises by modeling the errors of georeferenced points with an appropriate probability distribution and modifying the traditional dominance criterion used by that technique. The method is applied to a scenario in which the coordinates are set by a geocoding process in a sample of schools in a speciï¬ c Brazilian city. It enables one to choose the level of conï¬ dence in which a point is removed from the skyline solution (the location recommendation).