Related papers: Generalized Exponential Function and some of its A…
We propose a family of multivariate Gaussian process models for correlated outputs, based on assuming that the likelihood function takes the generic form of the multivariate exponential family distribution (EFD). We denote this model as a…
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
Four new probability models are derived which generalize the common univariate continuous distributions. Classical distributional measures are derived from Hoel, et al., Introduction to Probability Theory, 1971. Measures include probability…
In this paper, we introduce the generalized Gompertz-power series class of distributions which is obtained by compounding generalized Gompertz and power series distributions. This compounding procedure follows same way that was previously…
A new class of distributions, called Generalized One Parameter Polynomial Exponential-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented.…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
A generalized matrix-pencil approach is proposed for the estimation of complex exponential components with segmented signal samples, which is very efficient and provides super-resolution estimations. It is applicable to the signals sampled…
The aim of this paper, is to define a bivariate exponentiated generalized linear exponential distribution based on Marshall-Olkin shock model. Statistical and reliability properties of this distribution are discussed. This includes…
Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
This paper investigates in depth the fundamental properties of the two-parameter generalized Euler logarithm and its inverse, the associated deformed $(a,b)$-exponential function. We systematically clarify the parameter domains that…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
In this paper, we introduce a new concept of generalized convexity for E-differentiable vector optimization problems. Namely, the notion of exponentially E-invexity is defined. Further, some properties and results of exponentially E-invex…
We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the…
In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…