Journal of Data Science

Abstract: In this paper we introduce a Bayesian analysis of a spherical distri bution applied to rock joint orientation data in presence or not of a vector of covariates, where the response variable is given by the angle from the mean and the covariates are the components of the normal upwards vector. Standard simulation MCMC (Markov Chain Monte Carlo) methods have been used to obtain the posterior summaries of interest obtained from Win Bugs software. Illustration of the proposed methodology are given using a simulated data set and a real rock spherical data set from a hydroelectrical site.

Abstract: A new extension of the generalized gamma distribution with six parameter called the Kummer beta generalized gamma distribution is introduced and studied. It contains at least 28 special models such as the beta generalized gamma, beta Weibull, beta exponential, generalized gamma, Weibull and gamma distributions and thus could be a better model for analyzing positive skewed data. The new density function can be expressed as a linear combination of generalized gamma densities. Various mathematical properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating function, mean deviations, entropy, density function of the order statistics and their moments are derived. The elements of the observed information matrix are provided. We discuss the method of maximum likelihood and a Bayesian approach to fit the model parameters. The superiority of the new model is illustrated by means of three real data sets.

Abstract: Breast cancer is the second most common type of cancer in the world (World Cancer Report, 2014 a, b). The evolution of breast cancer treatment usually allows a longer life of patients as well in many cases a relapse of the disease. Usually medical researchers are interested to analyze data denoting the time until the occurrence of an event of interest such as the time of death by cancer in presence of right censored data and some covariates. In some situations, we could have two lifetimes associated to the same patient, as for example, the time free of the disease until recurrence and the total lifetime of the patient. In this case, it is important to assume a bivariate lifetime distribution which describes the possible dependence between the two observations. We consider as an application, different parametric bivariate lifetime distributions to analyze a breast cancer data set considering continuous or discrete data. Inferences of interest are obtained under a statistical Bayesian approach. We get the posterior summaries of interest using existing MCMC (Markov Chain Monte Carlo) methods. The main goal of the study, is to compare the bivariate continuous and discrete distributions that better describes the breast cancer lifetimes.

Abstract: The concept of frailty provides a suitable way to introduce random effects in the model to account for association and unobserved heterogeneity. In its simplest form, a frailty is an unobserved random factor that modifies multiplicatively the hazard function of an individual or a group or cluster of individuals. In this paper, we study positive stable distribution as frailty distribution and two different baseline distributions namely Pareto and linear failure rate distribution. We estimate parameters of proposed models by introducing Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique. In the present study a simulation is done to compare the true values of parameters with the estimated value. We try to fit the proposed models to a real life bivariate survival data set of McGrilchrist and Aisbett (1991) related to kidney infection. Also, we present a comparison study for the same data by using model selection criterion, and suggest a better model.

Abstract:In medical literature, researchers suggested various statistical procedures to estimate the parameters in claim count or frequency model. In the recent years, the Poisson regression model has been widely used particularly. However, it is also recognized that the count or frequency data in medical practice often display over-dispersion, i.e., a situation where the variance of the response variable exceeds the mean. Inappropriate imposition of the Poisson may underestimate the standart errors and overstate the significance of the regression parameters, and consequently, giving misleading inference about the regression parameters. This article suggests the Negative Binomial (NB) and Conway-Maxwell-Poisson (COM-Poisson) regression models as an alternatives for handling overdispersion. All mentioned regression models are applied to simulation data and dataset of hospitalization number of people with schizophrenia, the results are compared.