Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Educational levels and the functional dependence of ischemic stroke survivors

We evaluated the functional dependence of stroke survivors from the Study of Stroke Mortality and Morbidity, using the Rankin Scale. Out of 355 ischemic stroke survivors (with a mean age of 67.9 years), 40% had some functional dependence at 28 days and 34.4% had some functional dependence at 6 months. Most predictors of physical dependence were identified at 28 days. These predictors were: low levels of education [illiterate vs. >= 8 years of education, multivariate odds ratio (OR) = 3.7; 95% confidence interval (95%CI): 1.60-8.54] and anatomical stroke location (total anterior circulation infarct, OR = 16.9; 95%CI: 2.93-97.49). Low levels of education and ischemic brain injury influenced functional dependence in these stroke survivors. Our findings reinforce the necessity of developing strategies for the rehabilitation of stroke patients, more especially in formulating specific strategies for care and treatment of stroke survivors with low socioeconomic status.