Related papers: Linear Statistics with Random Coefficients and Cha…
We provide new characterizations of two-points and some related distributions. We use properties of independence and/or identity of the distributions of suitable linear forms of random variables. Keywords: characterization of a…
There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
Let X be a locally compact Abelian group. We consider linear forms of independent random variables with values in X. In doing so, one of the coefficients of the linear forms is a random variable with a Bernoulli distribution. For some…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…
This paper introduces a new idea for constructing operators associated with a certain class of probability measures. Special cases include several know classical and noncommutative probability. The main example is derived from Feller [30,…
In this paper, we introduce the concept of hyperbolic valued random variables, their expectation and moments. We develop the hyperbolic analogue of Binomial and Poisson distributions. We study some of the properties of expectation on the…
This is a lightning introduction to some modern techniques used in the study of the statistical properties of hyperbolic dynamical systems. The emphasis is not in presenting a comprehensive theory but rather in fleshing out the main ideas…
The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…
Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…
We present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically…
In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial…
Although it is the generator distribution of the sixth natural exponential family with quadratic variance function, the Hyperbolic-Secant distribution is much less known than other distributions in the exponential families. Its lack of…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank…
We characterize certain noncommutative domains in terms of noncommutative holomorphic equivalence via a pseudometric that we define in purely algebraic terms. We prove some properties of this pseudometric and provide an application to free…
The hyperbolic secant distribution has several generalizations with applications in finance. In this study, we explore the dual geometric structure of one such generalization, namely the beta-logistic distribution. Recent findings also…
Hyperbolicity and dominated splitting are two of the most important concepts in the global analysis of differentiable dynamics. In this paper we give several equivalent characterizations of the dominated splitting and in particular we show…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
The paper presents some distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts. Utilizing these properties, we extend several known results and obtain some new…