Related papers: A General size-biased distribution
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
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 $m\in \mathbb{N}$,…
The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise $q$-Stirling's formula. The $\alpha $-divergence (or $q$-divergence) is uniquely derived from the generalized binomial…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…
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…
We introduce a special family of distributional alpha-densities and give a transversality criterion stating when their product is defined, closely related to Hormander's criterion for general distributions. Moreover, we show that for the…
In this paper, we extend Stein's method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the…
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
We study a symmetric generalization $\mathfrak{p}^{(N)}_k(\eta, \alpha)$ of the binomial distribution recently introduced by Bergeron et al, where $\eta \in [0,1]$ denotes the win probability, and $\alpha$ is a positive parameter. This…
We study the distribution functions of several classical error terms in analytic number theory, focusing on the remainder term in the Dirichlet divisor problem $\Delta(x)$. We first bound the discrepancy between the distribution function of…
We study the size, in terms of the Hausdorff dimension, of the subsets of $\mathbb T$ such that the Fourier series of a generic function in $L^1(\TT)$, $L^p(\TT)$ or in $\mathcal C(\mathbb T)$ may behave badly. Genericity is related to the…
In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
In this paper, we determine the density functions of nonsymmetrised doubly noncentral matrix variate beta type I and II distributions. The nonsymetrised density functions of doubly noncentral and noncentral bimatrix variate generalised beta…
New identity for fractional integrals have been defined. By using of this identity, we obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for s-convex, quasi-convex, m-convex functions via Riemann…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
Fujii obtained a formula for the average number of Goldbach representations with lower order terms expressed as a sum over the zeros of the Riemann zeta-function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…