Related papers: Geometric quantile-based measures of multivariate …
This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…
The $\mathcal{G}^0$ distribution is widely used for monopolarized SAR image modeling because it can characterize regions with different degree of texture accurately. It is indexed by three parameters: the number of looks (which can be…
How to distribute a set of points uniformly on a spherical surface is a very old problem that still lacks a definite answer. In this work, we introduce a physical measure of uniformity based on the distribution of distances between points,…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
The Guide to the Expression of Uncertainty in Measurement (GUM) mainly deals with measurement models having only a single output quantity. However, in many cases more than one output quantity is required, where all of them are related to a…
Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under…
To solve the problems in measuring coefficient of skewness related to extreme value, irregular distance from the middle point and distance between two consecutive numbers, "Rank skewness" a new measure of the coefficient of skewness has…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
In this paper we consider a semitetrad covariant decomposition of spherically symmetric spacetimes and find a governing hyperbolic equation of the Gaussian curvature of two dimensional spherical shells, that emerges due to the…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
Multivariate hypergeometric distribution arises frequently in elementary statistics and probability courses, for simultaneously studying the occurence law of specified events, when sampling without replacement from a finite population with…
We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot…
We formulate a class of angular Gaussian distributions that allows different degrees of isotropy for directional random variables of arbitrary dimension. Through a series of novel reparameterization, this distribution family is indexed by…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…