Related papers: New Modified Gamma and Beta Functions
In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of…
A simple closed-form approximation for the median of the beta distribution Beta(a, b) is introduced: (a-1/3)/(a+b-2/3) for (a,b) both larger than 1 has a relative error of less than 4%, rapidly decreasing to zero as both shape parameters…
In this paper we calculate some Generalized Selberg integrals. The answer is expressed in terms of $\Gamma$-functions. Integrals of this type serve as normalization constants or directly via undoing 2-D integrals for determination of…
We give closed-form expressions for the Dirichlet beta function at even positive integers and for the Dirichlet lambda function at odd positive integers, based on the function J(s) defined via convergent integral. We also show fundamental…
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient…
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.
This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.
This paper presents numerical values for auxiliary integrals and coefficients of the beta function in the three-loop approximation for a four-dimensional model with a quartic interaction, using a special type of regularization function. The…
We approach the Generalized Beta (GB) family of distributions using a mean-reverting stochastic differential equation (SDE) for a power of the variable, whose steady-state (stationary) probability density function (PDF) is a modified GB…
We offer two new Mellin transform evaluations for the Riemann zeta function in the region $0<\Re(s)<1.$ Some discussion is offered in the way of evaluating some further Fourier integrals involving the Riemann xi function.
We derive a closed form solution for the Kullback-Leibler divergence between two generalized gamma distributions. These notes are meant as a reference and provide a guided tour towards a result of practical interest that is rarely…
Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
The applications of the recent results obtained in the theory of generalized Lambert functions, to the mean field theory of ferromagnetism are presented. As a consequence, all the predictions of the Weiss theory of ferromagnetism can be…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
We introduce a $p$-adic analogue of the incomplete gamma function. We also introduce quantities ($m$-values) associated to a function on natural numbers and prove a new characterization of $p$-adic continuity for functions with $p$-integral…
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…
We define a generalisation of the completed Riemann zeta function in several complex variables. It satisfies a functional equation, shuffle product identities, and has simple poles along finitely many hyperplanes, with a recursive structure…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
In this paper, we define a q-adic factorial and we demonstrate some properties of a generalized p-adic gamma function. Also, some numerical examples have been given