Abstract

Abstract
An important problem in directional statistics is to test the null hypothesis of a common mean direction for several populations. The Analysis of Variance (ANOVA) test for vectorial data may be used to test the hypothesis of the equality of the mean directions for several von Mises-Fisher populations. As this test is valid only for large concentrations, we propose in this paper to apply the resampling techniques of bootstrap and permutation to the ANOVA test. We carried out an extensive simulation study in order to evaluate the performance of the ANOVA test with the resampling techniques, for several sphere dimensions and different sample sizes and we compare with the usual ANOVA test for data from von Mises-Fisher populations. The purpose of this simulation study is also to investigate whether the proposed tests are preferable to the ANOVA test, for low concentrations and small samples. Finally, we present an example with spherical data.

Abstract
In real situations the evaluation of the global quality of either a product or a service depends on more than one quality characteristic. In order to monitor the variability of multivariate processes and identify the variables responsible for changes in the process, we will use the STATIS (Structuration des Tableaux A Trois Indices de la Statistique) methodology, a three-way data analysis method. For this purpose we consider a control chart based on a similarity measure between two positive semi-definite matrices, the RV coefficient, and we evaluate the performance of this control chart for monitoring multivariate normal data.

Abstract
A control chart based on the quantile function to monitor the shape parameter of a Weibull distribution is proposed and its performance is analyzed by Monte Carlo simulation. The importance of monitoring the shape parameter even when the other parameters of the Weibull distribution are assumed known is further enhanced, together with motivating examples. © 2014 Proceedings of COMPSTAT 2014 - 21st International Conference on Computational Statistics. All rights reserved.