The definition and a number of inequalities for a standard DE were illustrated in [9, 3, 7]. Furthermore, in [1, 6] the initial definition and results on weighted entropy was introduced. Following [10, 5, 8, 11], recently in [4, 2, 13, 14, 15], a similar method with standard DE drives to emerge certain properties and applications of information-theoretical weighted entropies with a number of de...

The Gaussian distribution is commonly used to model uncertainty for all kind of problems. However, directional data like fiber orientations in injection molding simulations the canonical choice so called angular central (ACG) distribution, which arises as analytical solution Jeffrey's equation orientation a elliptical suspended flow field. Computations are favorably performed using moments dens...

We introduce a family of polynomials that generalizes the Bell polynomials, in connection with the combinatorics of the central moments of the Poisson distribution. We show that these polynomials are dual of the Charlier polynomials by the Stirling transform, and we study the resulting combinatorial identities for the number of partitions of a set into subsets of size at least 2.

Abstract This paper presents an iterative formulation to compute the central moments of matrix Fisher distribution on three dimensional special orthogonal group up arbitrary order.

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues...

We study a generalized Friedman’s urn model with multiple drawings of white and blue balls. After a drawing, the replacement follows a policy of opposite reinforcement. We give the exact expected value and variance of the number of white balls after a number of draws, and determine the structure of the moments. Moreover, we obtain a strong law of large numbers, and a central limit theorem for t...

The Gompertz distribution is widely used to describe the distribution of adult deaths. Previous works concentrated on formulating approximate relationships to characterize it. However, using the generalized integro-exponential function Milgram (1985) exact formulas can be derived for its moment-generating function and central moments. Based on the exact central moments, higher accuracy approxim...

We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in random trees of logarithmic height. The approach is simple but gives very precise estimates for expected width, central moments of the width, and almost sure convergence. It is widely applicable to random trees of logarithmic height, including...