Related papers: Directional distributions and the half-angle princ…
The need for statistical models of orientations arises in many applications in engineering and computer science. Orientational data appear as sets of angles, unit vectors, rotation matrices or quaternions. In the field of directional…
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…
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…
The paper considers the distribution of a general linear combination of central and non-central chi-square random variables by exploring the branch cut regions that appear in the standard Laplace inversion process. Due to the original…
A comprehensive toolkit is developed for regression analysis of directional data based on a flexible class of angular Gaussian distributions. Informative testing procedures for isotropy and covariate effects on the directional response are…
We demonstrate that certain astrophysical distributions can be modelled with the truncated Weibull distribution, which can lead to some insights: in particular, we report the average value, the $r$th moment, the variance, the median, the…
In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…
Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between…
Calculation of the distribution of the average value of a Gaussian random field in a finite domain is carried out for different cases. The results of the calculation demonstrate a strong dependence of the width of the distribution on the…
We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…
We consider the nodal domains of Gaussian random waves in two dimensions. We present a method to calculate the distribution of the number of nodal domains and the average connectivity with the help of auxiliary Potts-spins. An analytical…
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those…
Directional or Circular statistics are pertaining to the analysis and interpretation of directions or rotations. In this work, a novel probability distribution is proposed to model multidimensional sparse directional data. The Generalised…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
Entangled photons generated by spontaneous parametric down conversion inside a nonlinear crystal exhibit a complex spatial photon count distribution. A quantitative description of this distribution helps with the interpretation of…
The angular halfspace depth (ahD) is a natural modification of the celebrated halfspace (or Tukey) depth to the setup of directional data. It allows us to define elements of nonparametric inference, such as the median, the inter-quantile…
This paper extends the notion of the matrix angular central distribution (MACG) to the complex case. We start by considering the normally distributed random complex matrix ($Z$) and show that is the orientation ($H_Z=Z(Z'Z)^{-1}$) has…
We define and study a family of distributions with domain complete Riemannian manifold. They are obtained by projection onto a fixed tangent space via the inverse exponential map. This construction is a popular choice in the literature for…
Non-Gaussian distributions are commonly observed in collisionless space plasmas. Generating samples from non-Gaussian distributions is critical for the initialization of particle-in-cell simulations that investigate their driven and…
An angular clustering method based on image processing is proposed in this paper. It is used to identify clusters in 2D representations of propagation channels. The approach uses operations such as watershed segmentation and is particularly…