Related papers: Boolean Extremes and Dagum Distributions
We prove optimal constant over root $n$ upper bounds for the maximal probabilities of $n$th convolution powers of discrete uniform distributions.
This paper investigates the moment monotonicity property of Weibull, Gamma, and Log-normal distributions. We provide the first complete mathematical proofs for the monotonicity of the function $E(X^n)^{\frac{1}{n}}$ specific to these…
The randomization effect of the two-way (particle-flow) interaction has been studied and quantified using the notion of distributed chaos and the results of numerical simulations and laboratory measurements. It is shown, in particular, that…
We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…
We introduce a quantum convolution and a conceptual framework to study states in discrete-variable (DV) quantum systems. All our results suggest that stabilizer states play a role in DV quantum systems similar to the role Gaussian states…
The dynamics of a tagged particle immersed in a fluid of particles of the same size but different mass is studied when the system is confined between two hard parallel plates separated a distance smaller than twice the diameter of the…
The velocity distribution of inelastic granular gas is examined numerically on two dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributions in nature and describes a large number of physical, biological and even sociological phenomena. The origin of this distribution is…
This article investigates the collisionless Boltzmann equation up to second order in the cosmological perturbations. It describes the gauge dependence of the distribution function and the construction of a gauge invariant distribution…
Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to…
Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…
We study the zeroes of a family of random holomorphic functions on the unit disc, distinguished by their invariance with respect to the hyperbolic geometry. Our main finding is a transition in the limiting behaviour of the number of zeroes…
The maximum likelihood degree of a statistical model refers to the number of solutions, where the derivative of the log-likelihood function is zero, over the complex field. This paper examines the maximum likelihood degree of the parameter…
A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the…
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise…
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained…
The Euler and Navier-Stokes fluid mechanics equations are derived using a modified statistical mechanical approach using theory taken from the Chapman-Enskog perturbation analysis used to support the lattice Boltzmann method. Additional…
The theory of homogeneously driven granular gases of hard particles predicts that the stationary state is characterized by a velocity distribution function with overpopulated high-energy tails as compared to the exponential decay valid for…