Related papers: Distributions: a spherical co-ordinates approach
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…
We review some probabilistic properties of the sum-of-digits function of random integers. New asymptotic approximations to the total variation distance and its refinements are also derived. Four different approaches are used: a classical…
Tractable generalizations of the Gaussian distribution play an important role for the analysis of high-dimensional data. One very general super-class of Normal distributions is the class of $\nu$-spherical distributions whose random…
The concept of median/consensus has been widely investigated in order to provide a statistical summary of ranking data, i.e. realizations of a random permutation $\Sigma$ of a finite set, $\{1,\; \ldots,\; n\}$ with $n\geq 1$ say. As it…
This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t…
A random walk on a directed graph gives a Markov chain on the vertices of the graph. An important question that arises often in the context of Markov chain is whether the uniform distribution on the vertices of the graph is a stationary…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we…
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. Aside from a few special cases, the density function for…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
In the framework of distributionally generalized quantum theory, the object $H\psi$ is defined as a distribution. The mathematical significance is a mild generalization for the theory of para- and pseudo-differential operators (as well as a…
A class of discrete probability distributions contains distributions with limited support, i.e. possible argument values are limited to a set of numbers (typically consecutive). Examples of such data are results from subjective experiments…
In this paper we define and examine the power of the {\em conditional-sampling} oracle in the context of distribution-property testing. The conditional-sampling oracle for a discrete distribution $\mu$ takes as input a subset $S \subset…
With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…
In this paper we will study integrability of distributions whose primitives are left regulated functions and locally or globally integrable in the Henstock--Kurzweil, Lebesgue or Riemann sense. Corresponding spaces of distributions and…
The theory of slice regular (also called hyperholomorphic) functions is a generalization of complex analysis originally given in the quaternionic framework, and then further extended to Clifford algebras, octonions, and to real alternative…