Related papers: Bandwidth of Gamma-Distribution-Shaped Functions v…
Based on a Problem and its solution published on the pages of SIAM Review, we give an interesting integral representation for the Lambert $W$ function in this short note. In particular, our result yields a new integral representation for…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to…
The Gamma-Gamma (GG) distribution has recently attracted the interest within the research community due to its involvement in various communication systems. In the context of RF wireless communications, GG distribution accurately models the…
The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new" special function that has recently been the subject of an extended upsurge in interest and applications. In this note, I point out that the Lambert W function can…
An experimental investigation of sub-wavelength imaging by a wire medium slab is performed. A complex-shaped near field source is used in order to test imaging performance of the device. It is demonstrated that the ultimate bandwidth of…
The incomplete moment generating function (IMGF) has paramount relevance in communication theory, since it appears in a plethora of scenarios when analyzing the performance of communication systems. We here present a general method for…
In this paper we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy…
I discuss comments and claims made in Stehlik and Hermann (2015) about skewed Lambert W x F random variables and the IGMM algorithm. I clarify misunderstandings about the definition and use of Lambert W x F distributions and show that most…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W) = We^W$, provides…
It is shown that, for a Hamiltonian with a band structure, the half width of local spectral density of states, or strength function, is closely related to the width of the nonperturbative (NPT) parts of energy eigenfunctions. In the…
The gravitational evolution of the cosmic one-point probability distribution function (PDF) has been estimated using an analytic approximation that combines gravitational perturbation theory with the Edgeworth expansion around a Gaussian…
The gravitational evolution of the cosmic one-point Probability Distribution Function (PDF) can be estimated using an analytic approximation that combines gravitational Perturbation Theory (PT) with the Edgeworth expansion around a Gaussian…
Photon counts statistics have recently been proven to provide a sensitive observable for characterizing gamma-ray source populations and for measuring the composition of the gamma-ray sky. In this work, we generalize the use of the standard…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
We find an inverse factorial series expansion for the ratio of products of gamma functions whose arguments are linear functions of the variable. We a give recurrence relation for the coefficients in terms of the N{\o}rlund-Bernoulli…
The gamma distribution arises frequently in Bayesian models, but there is not an easy-to-use conjugate prior for the shape parameter of a gamma. This inconvenience is usually dealt with by using either Metropolis-Hastings moves, rejection…
Various approaches to the numerical representation of the Incomplete Gamma Function F_m(z) for complex arguments z and small integer indexes m are compared with respect to numerical fitness (accuracy and speed). We consider power series,…
The Fisher-Bingham distribution ($\mathrm{FB}_8$) is an eight-parameter family of probability density functions (PDF) on $S^2$ that, under certain conditions, reduce to spherical analogues of bivariate normal PDFs. Due to difficulties in…