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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]

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]

Multivariate lifetime data are common in many applications, especially in medical and engineering studies. In this paper, we consider a trivariate Marshall-Olkin-Weibull distribution to model trivariate data in presence of right censored data. Maximum likelihood and Bayesian methods are used to get the parameter estimators of interest. An extensive simulation study was performed to verify the effectiveness of the maximum likelihood estimators. Reliability data sets related to fiber failure strengths were considered to illustrate the performance of the proposed model under the classical and Bayesian approaches. As a result, note that the trivariate Marshall-Olkin-Weibull model could be considered as a good alternative to model trivariate lifetime data, especially under a Bayesian approach which could be of interest for the reliability analysis, as observed with the real data application in industrial engineering presented in the study or any other area of interest. [ABSTRACT FROM AUTHOR]

In recent years, the use of copulas has grown rapidly, especially in survival analysis. In this paper, we introduce a bivariate modified Weibull distribu-tion derived from the Farlie{Gumbel{Morgenstern (FGM), a copula function commonly used to model very weak linear dependences. Considering the presence of non censored data and censored data, an extensive simulation study was developed to check the performance of the maximum likelihood method in estimating the parameters of the proposed model. Maximum like-lihood and Bayesian approaches for the estimation of the model parameters are presented. In the Bayesian analysis, the posterior distributions of the pa-rameters are estimated using Markov chain Monte Carlo (MCMC) method-ology. An example, considering a real data set, is introduced to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Simulation studies are important statistical tools used to inves-tigate the performance, properties and adequacy of statistical models. The simulation of rightcensored time-to-event data involves the generation of two independent survival distributions, where the rst distribution repre-sents the uncensored survival times and the second distribution represents the censoring mechanism. In this brief report we discuss how we can make it so that the percentage of censored data is previously de ned. The described method was used to generate data from a Weibull distribution, but it can be adapted to any other lifetime distribution. We further presented an R code function for generating random samples, considering the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce bivariate lifetime models derived from copula functions considering two copula functions, the Farlie Gumbel Morgenstern (FGM) commonly used to model very weak linear dependences and the Gumbel-Barnett copula which models very weak non necessarily linear dependences. Considering the presence of cure fractions for both lifetimes, censored data and covariates, we use standard MCMC (Markov Chain Monte Carlo) methods to get a Bayesian analysis for the proposed models. This new modelling approach gives a great flexibility of fit for bivariate data, since we could assume any existing parametric marginal lifetime distribution for the bivariate lifetimes as standard Weibull, log-normal, gamma, generalized gamma, generalized Weibull or generalized F distributions. An example, considering a medical data set is introduced to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper we introduce bivariate Weibull distributions derived from copula functions in presence of cure fraction, censored data and covariates. Two copula functions are explored: the FGM (Farlie - Gumbel Morgenstern) copula and the Gumbel copula. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a medical data set. [ABSTRACT FROM AUTHOR]

In general, the identification of probability distributions for time between arrivals and the covariates that affect them, get a superficial treatment in papers on production engineering. The main goal of this paper is to analyze the data on the time between arrivals for batches at the quality control department in a food company. A Weibull distribution, with two parameters, was used in the statistical modeling - a quantitative approach. Scale and shape was estimated by the Maximum Likelihood Method. A regression Weibull model was considered to evaluate inferences for the mean and median times between arrivals and to detect important factors affecting the variability in data sets. Considering some covariates, the Weibull distribution was found to have a good fit for the data. These results allow for a more reliable modeling of the quality control department for discrete event simulation. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents estimates for the parameters included in long-term mixture and non-mixture lifetime models, applied to analyze survival data when some individuals may never experience the event of interest. We consider the case where the lifetime data have a two-parameters exponentiated exponential distribution. The two-parameter exponentiated exponential or the generalized exponential distribution is a particular member of the exponentiated Weibull distribution introduced by [31]. Classical and Bayesian procedures are used to get point and confidence intervals of the unknown parameters. We consider a general survival model where the scale, shape and cured fraction parameters of the exponentiated exponential distribution depends on covariates. [Copyright &y& Elsevier]