This paper presents Bayesian directional data modeling via the skew-rotationally-symmetric Fisher-von Mises-Langevin (FvML) distribution. The prior distributions for the parameters are a pivotal building block in Bayesian analysis, therefore, the impact of the proposed priors will be quantified using the Wasserstein Impact Measure (WIM) to guide the practitioner in the implementation process. For the computation of the posterior, modifications of Gibbs and slice samplings are applied for generating samples. We demonstrate the applicability of our contribution via synthetic and real data analyses. Our investigation paves the way for Bayesian analysis of skew circular and spherical data.
Abstract. In this paper, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O((log n) −λ ) for some λ > 0,. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.
Existing circular and toroidal distributions are mostly symmetric; however, many datasets possess asymmetric patterns. Due to the increasing need for asymmetric distributions in recent times, driven by complex modern datasets, in this chapter a new approach is introduced to generate skewed distributions from symmetric distributions, for modeling both circular and toroidal skewed data. This new family of asymmetric distributions, called generalized skew-symmetric distributions, includes some well-known distributions as special cases, such as the circular models of Umbach
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.