Abstract

Abstract
We consider n individuals described by p variables, represented by points of the surface of unit hypersphere. We suppose that the individuals are fixed and the set of variables comes from a mixture of bipolar Watson distributions. For the mixture identification, we use EM and dynamic clusters algorithms, which enable us to obtain a partition of the set of variables into clusters of variables.Our aim is to evaluate the clusters obtained in these algorithms, using measures of within-groups variability and between-groups variability and compare these clusters with those obtained in other clustering approaches, by analyzing simulated and real data.

Abstract
This paper presents the main concepts and results of a Master thesis in Data Analysis which aims to analyze the evolution of some developed countries and also of some emerging countries that are members of the Organisation for Economic Co-operation and Development (OECD) in what concerns some indicators or variables of well-being during the period 2011-2015, through the STATIS (Structuring Three-way data sets in Statistics) methodology. This methodology allows to analyze the presence of a common structure in several data tables obtained over time, to identify the differences and similarities along the period of time under study and according to well-being indicators included in the "Your Better Life Index" of the OECD, and to analyze the trajectories of the countries.

Abstract
We consider two sampling plans by variables to inspect batches of products from an industrial process under a context of unknown distribution underlying the measurements of the quality characteristic under study. Through the use of the bootstrap methodology and Monte Carlo simulations we evaluate and compare the performance of those sampling plans in terms of probability of acceptance of lots and average outgoing quality level.

Abstract
The problem of testing the null hypothesis of a common direction across several populations defined on the hypersphere arises frequently when we deal with directional data. We may consider the Analysis of Variance (ANOVA) for testing such hypotheses. However, for the Watson distribution, a commonly used distribution for modeling axial data, the ANOVA test is only valid for large concentrations. So we suggest to use alternative tests, such as bootstrap and permutation tests in ANOVA. Then, we investigate the performance of these tests for data from Watson populations defined on the hypersphere.

Abstract
Sensory tests are quality assurance tools commonly used to measure and/or detect the presence of abnormal characteristics perceived through the senses in lots of raw material and final products in many manufacturing and food industries. In this paper two acceptance sampling plans for sensory evaluation are designed, and an illustration of the performance of such plans applied to a real data set is presented.