Related papers: Broadly discrete stable distributions
In this paper we give a first attempt to define and study stable distributions with respect to the weak generalized convolution, focusing our attention on the symmetric weakly stable distribution. As in the case of the classical…
We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential families to…
Using the LePage representation, a strictly stable random element in a Banach space with $\alpha\in(0,2)$ can be represented as a sum of points of a Poisson process. This point process is union-stable, i.e. the union of its two independent…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
In this article, we develop a new class of multivariate distributions adapted for count data, called Tree P\'olya Splitting. This class results from the combination of a univariate distribution and singular multivariate distributions along…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…
In this paper, a new natural discrete version of the one parameter polynomial exponential family of distributions have been proposed and studied. The distribution is named as Natural Discrete One Parameter Polynomial Exponential (NDOPPE)…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
In this article we introduce associative Look-Up Tables. With their help, pseudo sums are correctly determined. The set of limit distributions in a pseudo-summation scheme of i.i.d. random variables is described. Also, two special cases…
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…