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This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull–Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull–Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information. [ABSTRACT FROM AUTHOR]

The use of semiparametric or transformation models has been considered by many authors in the analysis of lifetime data in the presence of censoring and covariates as an alternative and generalization of the usual proportional hazards, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. The inferences for the proportional hazards model introduced by Cox (1972) are usually obtained by maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox (Cox, 1975). In this study, we consider a hierarchical Bayesian analysis of the proportional hazards model assuming the complete likelihood function obtained from a transformation model considering the unknown hazard function as a latent unknown variable under a Bayesian approach. Some applications with real time medical data illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In the analysis of financial market data, random variations in price movements can share non-trivial statistical properties as observed for the distributions of returns, with possibility of absence of autocorrelations in asset returns, volatility in blocks and presence of asymmetry between rises and falls of stock values. Asset price fluctuations are usually investigated using time series models to obtain inferences about interest rates and future forecasts. In this study we consider the use of existing probability distributions to model run lengths and absolute historical price run returns as an alternative to the use of usual time series models with applications for time series obtained from the NYSE stock exchange for three private banks located in the Brazil in the period from July 19, 2013, to July 19, 2018. We assume discrete Weibull distributions as an alternative to the exponential law commonly used in this type of analysis. Under this modeling approach it is possible to obtain information about the structure of the market such as the probability of the stock market rising and falling daily and the magnitude of the returns. [ABSTRACT FROM AUTHOR]

The present study considers non-mixture models based on the discrete Burr XIII distribution to model recurrent event data in the presence of a cure fraction. In this context, we provide an alternative to the standard Cox proportional hazards model using a discretized distribution to analyze lifetime data assuming a non-mixture structure for cure rates. In a Bayesian setting, the proposed methodology was considered for analyzing a real dataset from a retrospective cohort study that aimed to evaluate specific clinical conditions that affect the lifetimes of 299 heart failure patients admitted to the Institute of Cardiology and Allied Hospital – Faisalabad, Pakistan (April-December, 2015). The model validation process was addressed using the Cox-Snell residuals, which allowed us to identify the suitability of the proposed non-mixture cure rate model. [ABSTRACT FROM AUTHOR]

In many practical situations, clinical diagnostic procedures include two or more biological traits whose outcomes are expressed on a continuous scale and are then dichotomized using a cut point. As measurements are performed on the same individual there is a likely correlation between the continuous underlying traits that can go unnoticed when the parameter estimation is done with the resulting binary variables. In this paper, we compare the performance of two different indexes developed to evaluate the dependence between diagnostic clinical tests that assume binary structure in the results with the performance of the binary covariance and two copula dependence parameters.Muchos procedimientos de diagnóstico clínico médico exigen la evaluación de dos o mas rasgos biológicos que se ven alterados ante la presencia de fenómenos de enfermedad o infección, los cuales se expresan en una escala continúa de medición con posterior dicotomización usando de un valor límite o punto de corte. Dado que las mediciones son realizadas en el mismo individuo, los resultados probablemente presenten dependencia de algún tipo, lo cual puede ser ignorado en la etapa de análisis de datos dada la presentación binaria de los datos. En este estudio comparamos el comportamiento de dos parámetros de dependencia presentes en funciones de cópula con el de la covarianza binaria y dos índices creados para medir dependencia entre pruebas diagnósticas de respuesta dicótoma.

In this paper, we show different parameters estimation forms for multiple linear regression model. We used clinical data, where the interest was to verify the relationship among the mechanical assay maximum stress with femoral mass, femoral diameter and group of ovariectomized Wistar rats. We used three inference methods: Classic inference, based on the least square method; bayesian inference, based on the Bayes theorem; and bootstrap inference, based on resampling processes.En este trabajo se muestran diferentes formas de estimación de parámetros para el modelo de regresión lineal múltiple. Para estimar los parámetros del modelo se utilizaron los datos de un ensayo clínico donde el interés era verificar la relación entre la tensión mecánica máxima del fémur con la masa y el diámetro femoral en un grupo experimental de ratas ovariectomizadas de la raza Rattus norvegicus albinos, variedad Wistar. Para estimar los parámetros del modelo se compararon tres métodos: la metodología clásica basada en el método de mínimos cuadrados, la metodología bayesiana, basada en el teorema de Bayes y la inferencia bootstrap basada en los procesos de remuestreo.Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

The statistical literature presents many continuous probability distributions with only one parameter, which are extensively used in the analysis of lifetime data, such as the exponential, the Lindley, and the Rayleigh distributions. Alternatively, the use of discretized versions of these distributions can provide a better fit for the data in many applications. As the novelty of this study, we present inferences for the discrete Bilal distribution (DB) with one parameter introduced by Altun et al. (2020) in the presence of right-censored data and cure fraction. We assume standard maximum likelihood methods based on asymptotic normality of the maximum likelihood estimators and also a Bayesian approach based on MCMC (Markov Chain Monte Carlo) simulation methods to get inferences for the parameters of the discrete BD distribution. The use of the proposed model was illustrated with three examples considering real medical lifetime data sets. From these applications, we concluded that the proposed model based on the discrete DB distribution has good performance even with the inclusion of a cure fraction in comparison to other existing discrete models, such as the DsFx-I, Lindley, Rayleigh, and Burr-Hatke probability distributions. Moreover, the model can be easily implemented in standard existing software, such as the R package. Under a Bayesian approach, we assumed a gamma prior distribution for the parameter of the DB discrete distribution. We also provided a brief sensitivity analysis assuming the half-normal distribution in place of the gamma distribution for the parameter of the DB distribution. From the obtained results of this study, we can conclude that the proposed methodology can be very useful for researchers dealing with medical discrete lifetime data in the presence of right-censored data and cure fraction. [ABSTRACT FROM AUTHOR]

In this study we consider some stochastic models and a Bayesian approach to analyze count time series data in the presence of one or more change-points. When the observed count data are all different of zero, it is possible to perform an analysis using linear regression models with normal distribution errors for the log-transformed data. When we have the presence of zero counts at different times, the statistical model based on the log-transformation is not suitable. Hence, in this case, it is possible to consider non-homogeneous Poisson processes (NHPP) models with a suitable rate function. In the present work we consider both models (linear regression and Poisson) to analyze three data sets. These sets are data recording the monthly visitors to New Zealand with the purpose of education, yearly tuberculosis incidence data from New York City, and monthly measles incidence data from Brazil. When the NHPP model is used a PLP (power law process) model is assumed for the intensity function. Additionally, in both models, the presence of change-points will be allowed. [ABSTRACT FROM AUTHOR]

Climate change has been observed worldwide in the last years. Among the different effects of climate change, rain precipitation is one of the effects that most challenge the population of all countries in the world. The main goal of this study is to introduce a data analysis of monthly rainfall data related to five countries in Central Asia (Kazakhstan, Kyrgyzstan, Tadjikistan, Turkmenistan and Uzbekistan) for a long period of time to discover the behavior of rain precipitation in these countries for each month of the year in the last decades and possible link with climate change. Since climate data are positive real values, Weibull regression models were fitted for the rain precipitation data (precipitation sums by climate station and year) under a classical inference approach in presence of some spatial factors as latitude and longitude of the climate stations in each country, temporal factors (linear year effects), altitude of the climate station and categorical factors (countries). The obtained results show that some factors have different effects in the monthly rainfall of the assumed countries during the follow-up assumed period, possibly linked to the climate change observed in the last decades worldwide. [ABSTRACT FROM AUTHOR]

En este artículo se presenta una breve descripción de modelos GARCH multivariados y se realizan inferencias de la volatilidad de series de tiempo usando un enfoque Bayesiano, utilizando algoritmos de simulación de Monte Carlo (MCMC). Como una aplicación para ilustrar la metodología propuesta, se analizan los log-retornos de IBOVESPA y Dow Jones Industrial en una base semanal de 04/27/1993 para 11/03/2008.

Ammonia nitrogen is a compound that in its abundance is related to the inadequate discharge of industrial and domestic effluents. Since high concentrations of ammonia nitrogen can directly affect the water quality or disturb the marine environment, this study examined the ammonia nitrogen concentrations in Columbia River, USA in a fixed period (from January, 2014 to January, 2020) related to some water factors. Some interesting conclusions were obtained in this study as the identification of dissolved oxygen (in mg/L), pH, specific conductivity (in umhos/cm), and temperature (in °C) as potential factors affecting the ammonia nitrogen concentrations in Columbia River which may alert authorities to keep restrictive strategies to control the advance of this kind of water pollution. The results of this study could be extended to other regions of the world, especially in more impoverished countries usually with precarious water pollution control systems with implications for public health. [ABSTRACT FROM AUTHOR]

In this study, the components of extra-Poisson variability are estimated assuming random effect models under a Bayesian approach. A standard existing methodology to estimate extra-Poisson variability assumes a negative binomial distribution. The obtained results show that using the proposed random effect model it is possible to get more accurate estimates for the extra-Poisson variability components when compared to the use of a negative binomial distribution where it is possible to estimate only one component of extra-Poisson variability. Some illustrative examples are introduced considering real data sets. [ABSTRACT FROM AUTHOR]

In this paper, it is introduced a new parametric distribution to be used in multivariate lifetime data analysis as an alternative for the use of some existing multivariate parametric models as the popular multivariate normal distribution which is the most widely used model assumed in the analysis of continuous multivariate data. Although the normal multivariate distribution has univariate marginal normal probability distributions and simple interpretations for all their parameters, it may not be well fitted by many data sets, especially in survival data applications, usually considering logarithm transformed data. In many cases the use of parametric multivariate discrete models could be more appropriate for the data analysis. In this paper, it is introduced a generalization of the bivariate Basu-Dhar geometric distribution to a trivariate case applied to count data. Some properties of this trivariate geometric distribution, including its marginal probability distributions, order statistics distributions, the probability generating function and some simulation studies are presented. It is also presented some discussion on an extension of the trivariate case for the multivariate case. Classical and Bayesian inferences are presented assuming censored or uncensored observations. To illustrate the proposed methodology, two applications with real lifetime data are considered as examples. [ABSTRACT FROM AUTHOR]

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost. [ABSTRACT FROM AUTHOR]