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.

Science and Society: The Case of Acceptance of Newtonian Optics in the Eighteenth Century

The present paper presents a historical study on the acceptance of Newton's corpuscular theory of light in the early eighteenth century. Isaac Newton first published his famous book Opticks in 1704. After its publication, it became quite popular and was an almost mandatory presence in cultural life of Enlightenment societies. However, Newton's optics did not become popular only via his own words and hands, but also via public lectures and short books with scientific contents devoted to general public (including women) that emerged in the period as a sort of entertainment business. Lectures and writers stressed the inductivist approach to the study of nature and presented Newton's ideas about optics as they were consensual among natural philosophers in the period. The historical case study presented in this paper illustrates relevant aspects of nature of science, which can be explored by students of physics on undergraduate level or in physics teacher training programs.

ANCIENT LAW – UM CLÁSSICO REVISITADO 150 ANOS DEPOIS

Este artigo pretende realçar a importância desempenhada pela obra de Henry James Sumner Maine na formação da antropologia jurídica e da sociologia do direito. Mediante a recuperação da tese central de sua obra Ancient Law, procura ressaltar o papel por ela desempenhado no delineamento de uma nova forma de abordagem da relação entre direito e sociedade. Para tanto, recupera traços gerais das análises de Norbert Rouland e de Niklas Luhmann acerca da importância das ideias do autor.