Related papers: Elliptical Tempered Stable Distribution and Fracti…
Based on the properties of distributions and measures with discrete support, we investigate temperate almost periodic distributions on the Euclidean space and connection with their Fourier transforms. We also study relations between the…
Elliptical distributions are a simple and flexible class of distributions that depend on a one-dimensional function, called the density generator. In this article, we study the non-parametric estimator of this generator that was introduced…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
The concept of temperature is one of the key ideas in describing the thermodynamical properties of a physical system. In classical statistical mechanics of ideal gases, the notion of temperature can be described in two different ways, the…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
The current definition of a conditional probability distribution enables one to update probabilities only on the basis of stochastic information. This paper provides a definition for conditional probability distributions with non-stochastic…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
This paper proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
The measurement of dispersion is one of the most fundamental and ubiquitous statistical concepts, in both applied and theoretical contexts. For dispersion measures, such as the standard deviation, to effectively capture the variability of a…
We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
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…