Related papers: On incomplete Gamma and Beta integrals
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…
Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics…
A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…
This paper investigates the efficiency of an alternative to ratio estimator under the super population model with uncorrelated errors and a gamma-distributed auxiliary variable. Comparisons with usual ratio and unbiased estimators are also…
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,…
In this article we prove a new elliptic hypergeometric integral identity. It previously appeared (as a conjecture) in articles by Rains, and Spiridonov and Vartanov. Moreover it gives a different proof of an identity in another article by…
In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…
This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…
The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms. The aim of this…
We describe a solution of the Gauss hypergeometric equation, $F(\alpha,\beta,\gamma;z)$ by power series in paramaters $\alpha,\beta,\gamma$ whose coefficients are $\Z$ linear combinations of multiple polylogarithms. And using the…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
We introduce the beta generalized normal distribution which is obtained by compounding the beta and generalized normal [Nadarajah, S., A generalized normal distribution, \emph{Journal of Applied Statistics}. 32, 685--694, 2005]…
A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…
Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero. Here we discuss a different method which is applicable in theories where one can perform a partial…
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0, 1) by the order statistics of a random sample of size n-1 from the uniform distribution U(0,1), for each n. A new…
We give different integral representations of the Lommel function $s_{\mu,\nu}(z)$ involving trigonometric and hypergeometric $_2F_1$ functions. By using classical results of Polya, we give the distribution of the zeros of $s_{\mu,\nu}(z)$…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.