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.

Abstract
The Von Mises-Fisher distribution defined on the hypersphere is one of the most used distributions for modelling vectorial data. If we reject the uniform distribution as a model for vectorial data, then the Von Mises-Fisher distribution is an alternative model. So we use this distribution as an alternative hypothesis in the study of the power of some tests of uniformity for some dimensions of the sphere.

Abstract
The von Mises-Fisher distribution is widely used for modeling directional data. In this article, we derive the discriminant rules based on this distribution to assign objects into pre-existing classes. We determine a distance between two von Mises-Fisher populations and we calculate estimates of the misclassification probabilities. We also analyze the behavior of the distance between two von Mises-Fisher populations and of the estimates of the misclassification probabilities when we modify the parameters of the populations or the samples size or the dimension of the sphere. Finally, we present an example with real spherical data available in the literature.

Abstract
The von Mises-Fisher distribution is widely used for modelling directional data. In this paper we propose goodness-of-fit methods for a concentrated von Mises-Fisher distribution and we analyse by simulation some questions concerning the application of these tests. We analyse the empirical power of the Kolmogorov-Smirnov test for several dimensions of the sphere, supposing as alternative hypothesis a mixture of two von Mises-Fisher distributions with known parameters. We also compare the empirical power of the Kolmogorov-Smirnov test with the Rao's score test for data on the sphere, supposing as alternative hypothesis, a mixture of two Fisher distributions with unknown parameters replaced by their maximum likelihood estimates or a 5-parameter Fisher-Bingham distribution. Finally, we give an example with real spherical data.

Abstract

Abstract
As the Watson distribution is much used for modeling axial data, it is important to investigate the existence of a possible outlier in samples from this distribution. So, we generalize to the hypersphere a test of discordancy of an outlier or several outliers en bloc available for the Watson distribution defined on the sphere. We also evaluate the performance of the test for some cases with the usual types of alternatives.