This article proposes the use of the Bayesian reference analysis to estimate the parameters of the generalized normal linear regression model. It is shown that the reference prior led to a proper posterior distribution, while the Jeffreys prior returned an improper one. The inferential purposes were obtained via Markov Chain Monte Carlo (MCMC). Furthermore, diagnostic techniques based on the Kullback–Leibler divergence were used. The proposed method was illustrated using artificial data and real data on the height and diameter of Eucalyptus clones from Brazil.

This article has earned an open data badge "Reproducible Research" for making publicly available the code necessary to reproduce the reported results. The results reported in this article could fully be reproduced.

This article focus on the analysis of the reliability of multiple identical systems that can have multiple failures over time. A repairable system is defined as a system that can be restored to operating state in the event of a failure. This work under minimal repair, it is assumed that the failure has a power law intensity and the Bayesian approach is used to estimate the unknown parameters. The Bayesian estimators are obtained using two objective priors know as Jeffreys and reference priors. We proved that obtained reference prior is also a matching prior for both parameters, i.e., the credibility intervals have accurate frequentist coverage, while the Jeffreys prior returns unbiased estimates for the parameters. To illustrate the applicability of our Bayesian estimators, a new data set related to the failures of Brazilian sugar cane harvesters is considered.

Based on the cohomology theory of groups, Andrade and Fanti defined in [1] an algebraic invariant, denoted by E(G, S, M ), where G is a group, S is a family of subgroups of G with infinite index and M is a Z 2 G-module. In this work, by using the homology theory of groups instead of cohomology theory, we define an invariant "dual" to E(G, S, M ), which we denote by E * (G, S, M ). The purpose of this paper is, through the invariant E * (G, S, M ), to obtain some results and applications in the theory of duality groups and group pairs, similar to those shown in Andrade and Fanti [2], and thus, providing an alternative way to get applications and properties of this theory.