Related papers: Cartesian Statistics on Spheres
Spatial orientation is a fundamental cognitive skill that relies on sensory information to update perceived direction. Understanding how sensory conditions influence directional accuracy is important for both cognitive science and the…
The distribution of visible matter in the universe, such as galaxies and galaxy clusters, has its origin in the week fluctuations of density that existed at the epoch of recombination. The hierarchical distribution of the universe, with its…
Model--based clustering for directional data data has attracted a lot of interest, but most methods utilize rotationally symmetric distributions. This paper suggests the use of elliptically symmetric distributions, namely the elliptically…
Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…
Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. By merging directional statistics…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
We introduce classifiers based on directional quantiles. We derive theoretical results for selecting optimal quantile levels given a direction, and, conversely, an optimal direction given a quantile level. We also show that the…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation. Unlike earlier covariance-based approaches for…
Analyzing point patterns with linear structures has recently been of interest in e.g. neuroscience and geography. To detect anisotropy in such cases, we introduce a functional summary statistic, called the cylindrical $K$-function, since it…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
Uniform distribution of the points has been of interest to researchers for a long time and has applications in different areas of Mathematics and Computer Science. One of the well-known measures to evaluate the uniformity of a given…
We study spatial clustering in a discrete, one-dimensional, stochastic, toy model of heavy particles in turbulence and calculate the spectrum of multifractal dimensions $D_q$ as functions of a dimensionless parameter, $\alpha$, that plays…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…
The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description…
Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations…