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By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
We explore a well-known integral representation of the logarithmic function, and demonstrate its usefulness in obtaining compact, easily-computable exact formulas for quantities that involve expectations and higher moments of the logarithm…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
The purpose of the present paper is to give unified expressions to the characteristic functions of all elliptical and related distributions. Those distributions including the multivariate elliptical symmetric distributions and some…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
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…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$. We will show that those…
Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential forms of n-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are…
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…
We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
In this paper, we establish a generalized Taylor expansion of a given function $f$ in the form $\displaystyle{f(x) = \sum_{j=0}^m c_j^{\alpha,\rho}\left(x^\rho-a^\rho\right)^{j\alpha} + e_m(x)}$ \noindent with $m\in \mathbb{N}$,…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
In this article, we present a new two-dimensional generalization of the gamma function based on the product of the one-dimensional generalized beta function and the one-dimensional generalized gamma function. As will become clear later,…