Related papers: Kumaraswamy and beta distribution are related by t…
Correlated proportions appear in many real-world applications and present a unique challenge in terms of finding an appropriate probabilistic model due to their constrained nature. The bivariate beta is a natural extension of the well-known…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
The unit-Lindley distribution was recently introduced in the literature as a viable alternative to the Beta and the Kumaraswamy distributions with support in (0; 1). This distribution enjoys many virtuous properties over the named…
A set of many identical interacting agents obeying a global additive constraint is considered. Under the hypothesis of equiprobability in the high-dimensional volume delimited in phase space by the constraint, the statistical behavior of a…
The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics.…
For a binary choice problem, the spatial coordination of decisions in an agent community is investigated both analytically and by means of stochastic computer simulations. The individual decisions are based on different local information…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
The p-variate gamma distribution in the sense of Krishnamoorthy and Parthasarathy exists for all positive integer degrees of freedom d and at least for all real values d > p-2, p > 1. For special structures of the "associated" covariance…
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it…
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical…
Some remarkable properties of the beta distribution are based on relations involving independence between beta random variables such that a parameter of one among them is the sum of the parameters of an other (see (1.1) et (1.2) below).…
We study when a given Gaussian random variable on a given probability space $(\Omega, {\cal{F}}, P) $ is equal almost surely to $\beta_{1}$ where $\beta $ is a Brownian motion defined on the same (or possibly extended) probability space. As…
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
An open stochastic system \`a la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeterminism caused by a fundamental lack of information. We…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
Mutualistic communities have an internal structure that makes them resilient to external per- turbations. Late research has focused on their stability and the topology of the relations between the different organisms to explain the reasons…
It is well known that, under some assumptions, the limit distribution of random block matrices and their partial transposition converges to the distributions of random variables in some noncommutative probability space. Using free…