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The classic censored regression model (tobit model) has been widely used in the economic literature. This model assumes normality for the error distribution and is not recommended for cases where positive skewness is present. Moreover, in regression analysis, it is well-known that a quantile regression approach allows us to study the influences of the explanatory variables on the dependent variable considering different quantiles. Therefore, we propose in this paper a quantile tobit regression model based on quantile-based log-symmetric distributions. The proposed methodology allows us to model data with positive skewness (which is not suitable for the classic tobit model), and to study the influence of the quantiles of interest, in addition to accommodating heteroscedasticity. The model parameters are estimated using the maximum likelihood method and an elaborate Monte Carlo study is performed to evaluate the performance of the estimates. Finally, the proposed methodology is illustrated using two female labor supply data sets. The results show that the proposed log-symmetric quantile tobit model has a better fit than the classic tobit model., 23 pages, 2 figures

The Birnbaum–Saunders (BS) distribution is a model that frequently appears in the statistical literature and has proved to be very versatile and efficient across a wide range of applications. However, despite the growing interest in the study of this distribution and the development of many articles, few of them have considered data with a dependency structure. To fill this gap, we introduce a new class of time series models based on the BS distribution, which allows modeling of positive and asymmetric data that have an autoregressive structure. We call these BS autoregressive moving average (BISARMA) models. Also included is a thorough study of theoretical properties of the proposed methodology and of practical issues, such as maximum likelihood parameter estimation, diagnostic analytics, and prediction. The performance of the proposed methodology is evaluated using Monte Carlo simulations. An analysis of real‐world data is performed using the methodology to show its potential for applications. The numerical results report the excellent performance of the BISARMA model, indicating that the BS distribution is a good modeling choice when dealing with time series data with positive support and asymmetrically distributed. Hence, it can be a valuable addition to the toolkit of applied statisticians and data scientists.

Autoregressive conditional duration (ACD) models have been preponderant when the subject is the modeling of high-frequency financial data. A prominent model that has demonstrated great adjustment c...

This study investigates three regression models based on the Birnbaum–Saunders distribution. The first model is obtained directly through the Birnbaum–Saunders distribution; the second model is obt...

Data with spatial dependence are often modeled by geoestatistical tools. In spatial regression, the mean response is described using explanatory variables with georeferenced data. This modeling frequently considers Gaussianity assuming the response follows a symmetric distribution. However, when this assumption is not satisfied, it is useful to suppose distributions with the same asymmetric behavior of the data. This is the case of the Birnbaum–Saunders (BS) distribution, which has been considered in different areas and particularly in environmental sciences due to its theoretical arguments. We propose a geostatistical model based on a new approach to quantile regression considering the BS distribution. Global and local diagnostic analytics are derived for this model. The estimation of model parameters and its local influence are conducted by the maximum likelihood method. Global influence is based on the Cook distance and it is compared to local influence, in both cases to detect influential observations, whose detection and removal can modify the conclusions of a study. We illustrate the proposed methodology applying it to environmental data, which shows this situation changing the conclusions after removing potentially influential observations. A comparison with Gaussian spatial regression is conducted.

In this paper, we derive a new continuous-discrete mixture regression model which is useful for describing highly censored data. This mixture model employs the Birnbaum-Saunders distribution for th...

The Birnbaum‐Saunders (BS) distribution is a model that frequently appears in the statistical literature and has proved to be very versatile and efficient across a wide range of applications. However, despite the growing interest in the study of the BS distribution, quantile regression modeling has not been considered for this distribution. To fill this gap, we introduce a class of quantile regression models based on the BS distribution, which allows us to describe positive and asymmetric data when a quantile must be predicted using covariates. We use an approach based on a quantile parameterization to generate the model, permitting us to consider a similar framework to generalized linear models, providing wide flexibility. The methodology proposed includes a thorough study of theoretical properties and practical issues, such as maximum likelihood parameter estimation and diagnostic analytics based on local influence and residuals. The performance of the residuals is evaluated by simulations, whereas an illustrative example of income data is conducted using the methodology to show its potential for applications. The numerical results report an adequate performance of the approach to quantile regression, indicating that the BS distribution is a good modeling choice when dealing with data that have both positive support and asymmetry. The economic implications of our investigation are discussed in the final section. Hence, it can be a valuable addition to the tool kit of applied statisticians and econometricians.

Este trabalho tem por objetivo analisar os contratos de concessão de praças de pedágio existentes no Estado do Rio Grande do Sul no período de 1998 até 2012, utilizando as informações obtidas do Relatório de Acompanhamento do Programa Estadual de Concessão Rodoviária do Rio Grande do Sul (PECR-RS). Para atingir tal meta, emprega-se o modelo de simulação proposto por Ng et al. (2007), o qual utiliza o procedimento de simulação de Monte Carlo, que permite inserir as informações contratuais, de modo a visualizar um possível comportamento das empresas durante a execução dos mesmos. Em suma, os resultados encontrados indicam que, para as praças analisadas com a taxa interna de retorno sendo aquela considerada no projeto básico de exploração, o tempo ótimo simulado foi igual ou menor do que aquele acordado contratualmente. Deve-se destacar que os contratos apresentados pelas concessionárias Rodo Sul e Santa Cruz seriam economicamente inviáveis dentro deste período de tempo.

In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in literature., 26 pages, 13 figures. Accepted for publication in Statistics: A Journal of Theoretical and Applied Statistics

Resumo O objetivo deste estudo foi avaliar os gastos catastróficos em saúde (GCS) e sua associação com condições socioeconômicas nos anos de 2009, 2011 e 2013 em Minas Gerais. Realizou-se um estudo transversal com dados da Pesquisa por Amostra de Domicílios. A variável dependente foi o GCS, em cada ano da pesquisa. Foram considerados catastróficos os gastos que ultrapassaram os limites de 10% e 25% da renda familiar. A associação entre o gasto catastrófico e as variáveis independentes foi testada por meio de regressão de Poisson. As prevalências de GCS variaram de 9,0% a 11,3% e 18,9% a 24,4% nos limites de 10% e 25%, sendo que o ano de 2011 apresentou os menores valores. A maior proporção dos gastos com saúde (94%) foi relativa aos gastos com medicamentos. A prevalência de CGS foi menor entre responsáveis pelo domicílio com maior escolaridade quando comparados àqueles sem estudo nos limites de 10% e 25%. Famílias com maior escore de riqueza apresentaram, nos dois limites, prevalência de GCS menores do que aquelas do primeiro quintil. Concluiu-se que os gastos com saúde afetaram significativamente o orçamento das famílias em Minas Gerais, sendo o gasto com medicamentos o principal componente dos gastos. Os achados reforçam o papel do SUS para minimizar o GCS e reduzir as desigualdades socioeconômicas. Abstract This study aimed to assess catastrophic health expenditures (CHE) and its association with socioeconomic conditions in 2009, 2011 and 2013 in Minas Gerais, Brazil. A cross-sectional study was carried out with data from the Household Sample Survey. The dependent variable was the CHE in each year of the survey. Expenditures that exceeded 10% and 25% of household income were considered catastrophic. The association between catastrophic health expenditure and independent variables was tested by the Poisson regression. The prevalence of CHE ranged from 9.0% to 11.3% and 18.9% to 24.4% within the limits of 10% and 25%, and 2011 recorded the lowest values. The largest proportion of health expenditure (94%) was related to the acquisition of medicines. The prevalence of CHE was lower among those responsible for the household with 12 or more years of study than those with no formal education. Households with a higher wealth score had, in both limits, lower prevalence of CHE than those of the first quintile. We concluded that health expenditures significantly affected the budget of households in Minas Gerais and the purchase of medicines was the main component of spending. The findings reinforce the role of the Brazilian Unified Health System (SUS) in minimizing CHE and reducing socioeconomic inequalities.

In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented. In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets., Comment: 17 pages, 7 figures

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.

Made available in DSpace on 2019-10-04T12:15:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-07-30 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) FAPEAM grants from the government of the State of Amazonas, Brazil Frailty models are used for modeling heterogeneity in the data analysis of lifetimes. Analysis that ignore frailty when it is present leads to incorrect inferences. In survival analysis, the distribution of frailty is generally assumed to be continuous and, in some cases, it may be appropriate to consider a discrete frailty distribution. Survival models induced by frailty with a continuous distribution are not appropriate for situations in which survival data contain experimental units where the event of interest has not happened even after a long period of observation (survival data with cure fraction), that is, situations with units having zero frailty. In this paper, we propose a new survival model induced by discrete frailty for modeling survival data in the presence of a proportion of long-term survivors and a single change point. We use the maximum likelihood method to estimate the model parameters and evaluate their performance by a Monte Carlo simulation study. The proposed approach is illustrated by analyzing a kidney infection recurrence data set. Univ Sao Paulo, Dept Math & Stat, Sao Carlos, SP, Brazil Univ Estadual Paulista, Dept Producing Engn, Sao Paulo, Brazil Univ Fed Amazonas, Dept Stat, Manaus, Amazonas, Brazil Univ Brasilia, Dept Stat, Brasilia, DF, Brazil Univ Estadual Paulista, Dept Producing Engn, Sao Paulo, Brazil

Birnbaum-Saunders models have been widely used to describe data following positive-skew distributions. In this article, we introduce a bivariate Birnbaum-Saunders distribution which has the mean as...

The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric distributions based on the family of continuous log-symmetric distributions. Some properties are discussed as well as estimation by the maximum likelihood method. A Monte Carlo simulation study is carried out to evaluate the performance of the estimators, and censored and uncensored data sets are used to illustrate the proposed methodology.

This paper introduces a cure rate survival model by assuming that the time to the event of interest follows a beta prime (BP) distribution and that the number of competing causes of the event of interest follows a negative binomial distribution. The proposed model provides a novel alternative to the existing cure rate regression models due to its flexibility, as the BP model can exhibit greater levels of skewness and kurtosis than these of the gamma and inverse Gaussian distributions. Moreover, the hazard rate function of this model can have an upside-down bathtub or an increasing shape. We approach both parameter estimation and local influence based on likelihood methods. In special, three perturbation schemes are considered for local influence. Numerical evaluation of the proposed model is performed by Monte Carlo simulations. In order to illustrate the potential for practice of our model, we apply it to the real medical dataset from a population-based study of incident cases of melanoma diagnosed in the state of Sao Paulo, Brazil.

OBJECTIVES This study assessed the moderating role of education on the relationship between multimorbidity and mortality among older adults in Brazil. STUDY DESIGN This was a cohort study. METHODS This study used data from 1768 participants of the Health, Well-Being and Ageing Cohort Study (SABE) who were assessed between 2006 and 2015. The Cox Proportional Risks Model was used to evaluate the association between multimorbidity (two or more chronic diseases) and mortality. An interaction term between education and multimorbidity was included to test the moderating role of education in this association. RESULTS The average follow-up time was 4.5 years, with a total of 589 deaths in the period. Multimorbidity increased the risk of mortality (hazard ratio [HR] 1.55, 95% confidence interval [CI] 1.27-1.91), and this association was not moderated by education (HR 1.06, 95% CI 1.00-1.13; P value = 0.07). CONCLUSIONS The impact of education and multimorbidity on mortality emphasises the need for an integrated approach directed towards the social determinants of health to prevent multimorbidity and its burden among older adults.

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. RESUMO Objetivo Investigar o potencial do instrumento Vulnerable Elders Survey para identificar idosos com expectativa de vida limitada, em ambientes de atenção primária à saúde. Método Estudo transversal realizado em todas as (nove) unidades de saúde de Jataí, Goiás (Brasil), no período de julho a dezembro de 2018. Obteve-se uma amostra de 407 idosos, considerando uma população ≥ 60 anos. Os participantes responderam a um questionário sobre características sociodemográficas e clínicas, incluindo o Vulnerable Elders Survey e o índice de Suemoto. Testamos a associação entre a expectativa de vida limitada e o Vulnerable Elders Survey usando análise de regressão logística múltipla. Resultados A idade média foi de 68,9 ± 6,6 anos, e 58,0% dos participantes eram mulheres. A pontuação média do Vulnerable Elders Survey foi de 2,0 ± 2,2, a pontuação média do índice de Suemoto foi de 31,5 ± 21,1%, e 17,2% dos participantes tinham expectativa de vida limitada. O Vulnerable Elders Survey foi associado a uma expectativa de vida limitada (OR = 1,57; p = < 0,0001). Conclusão O instrumento Vulnerable Elders Survey foi capaz de identificar idosos com expectativa de vida limitada em ambientes de atenção primária à saúde, além de poder auxiliar na detecção de idosos que não se beneficiariam com a triagem e o controle estrito de doenças crônicas. RESUMEN Objetivo Investigar el potencial del instrumento Vulnerable Elders Survey para identificar adultos mayores con esperanza de vida limitada en centros de atención primaria. Método Se trata de un estudio transversal realizado en todas las (nueve) unidades sanitarias de Jataí, Goiás (Brasil) de julio a diciembre de 2018. Se consideró una población de ≥ 60 años, de la cual se obtuvo una muestra de 407 adultos mayores. Los participantes respondieron un cuestionario sobre características sociodemográficas y clínicas, incluyendo el Vulnerable Elders Survey y el índice de Suemoto. Se comprobó la asociación entre la esperanza de vida limitada y el Vulnerable Elders Survey, mediante el análisis de regresión logística múltiple. Resultados La edad promedio era de 68,9 ± 6,6 años y el 58,0% de los participantes pertenecía al sexo femenino. La puntuación media del Vulnerable Elders Survey resultó en 2,0 ± 2,2; la puntuación media del índice de Suemoto, 31,5 ± 21,1% y el 17,2% de los participantes tenía una esperanza de vida limitada. El Vulnerable Elders Survey estaba asociado a una esperanza de vida limitada (OR = 1,57; p = < 0,0001). Conclusión El instrumento Vulnerable Elders Survey ha sido capaz de identificar a los adultos mayores con una esperanza de vida limitada en los centros de atención primaria, además de ayudar en la detección de aquellos adultos mayores que no se beneficiarían con el triaje y el control estricto de las enfermedades crónicas.

The Birnbaum–Saunders distribution has been widely used to model reliability and fatigue data. In this paper, we propose a regression of generalized linear models type based on a new bivariate Birnbaum–Saunders distribution. This is parameterized in terms of its means and allows data to be described in their original scale. We estimate the model parameters and carry out inference with the maximum likelihood method. A case study with real-world reliability data is conducted for motivating our investigation, illustrating the potential applications of the proposed results. We obtain a predictive model which can be a useful addition to the tool-kit of diverse practitioners, reliability engineers, applied statisticians, and data scientists.

A common assumption regarding the standard tobit model is the normality of the error distribution. However, asymmetry and bimodality may be present and alternative tobit models must be used. In this paper, we propose a tobit model based on the class of log-symmetric distributions, which includes as special cases heavy and light tailed distributions and bimodal distributions. We implement a likelihood-based approach for parameter estimation and derive a type of residual. We then discuss the problem of performing testing inference in the proposed class by using the likelihood ratio and gradient statistics, which are particularly convenient for tobit models, as they do not require the information matrix. A thorough Monte Carlo study is presented to evaluate the performance of the maximum likelihood estimators and the likelihood ratio and gradient tests. Finally, we illustrate the proposed methodology by using a real-world data set., 18 pages, 2 figures