Related papers: Computing the Kullback-Leibler Divergence between …
The Pinsker inequality lower bounds the Kullback--Leibler divergence $D_{\textrm{KL}}$ in terms of total variation and provides a canonical way to convert $D_{\textrm{KL}}$ control into $\lVert \cdot \rVert_1$-control. Motivated by…
Let $X$ have a Generalized Poisson distribution with mean $kb$, where $b$ is a known constant in the unit interval and $k$ is a discrete, non-negative parameter. We show that if an uninformative uniform prior for $k$ is assumed, then the…
The generalized Gaussian distribution that stems from information theory is studied. The log-Minkowski problem associated with generalized Gaussian distribution shall be introduced and solved.
We study the problem of spectrum estimation from transmission data of a known phantom. The goal is to reconstruct an x-ray spectrum that can accurately model the x-ray transmission curves and reflects a realistic shape of the typical energy…
An exact functional renormalization group flow equation is derived for the divergence functional which is a generalization of the Kullback-Leibler divergence to quantum field theories in the Euclidean domain. It compares distributions with…
A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivatives with a desired order of accuracy at nodal…
In this note, we derive the closed form formulae for moments of Student's t-distribution in the one dimensional case as well as in higher dimensions through a unified probability framework. Interestingly, the closed form expressions for the…
We derive the conjugate prior of the Dirichlet and beta distributions and explore it with numerical examples to gain an intuitive understanding of the distribution itself, its hyperparameters, and conditions concerning its convergence. Due…
In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our…
Differential equations of the form $\ddot R=-kR^\gamma$, with a positive constant $k$ and real parameter $\gamma$, are fundamental in describing phenomena such as the spherical gravitational collapse ($\gamma=-2$), the implosion of…
In this paper, some new upper bounds for Kullback-Leibler divergence(KL-divergence) based on $L^1, L^2$ and $L^\infty$ norms of density functions are discussed. Our findings unveil that the convergence in KL-divergence sense sandwiches…
Generalized Calabi-Gray manifolds are non-K\"ahler complex manifolds with very explicit geometry yet not being homogeneous. In this note, we demonstrate that how generalized Calabi-Gray manifolds can be used to answer some questions in…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a…
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,…
We study gradient bounds and other functional inequalities for the diffusion semigroup generated by Kolmogorov type operators. The focus is on two different methods: coupling techniques and generalized $\Gamma$-calculus techniques. The…
In this paper, we derive some upper and lower bounds and inequalities for the total variation distance (TVD) and the Kullback-Leibler divergence (KLD), also known as the relative entropy, between two probability measures $\mu$ and $\nu$…
We study the gradient flow for a relaxed approximation to the Kullback-Leibler (KL) divergence between a moving source and a fixed target distribution. This approximation, termed the KALE (KL approximate lower-bound estimator), solves a…
Let $ k >0 $ be an integer and $ Y $ a standard Gamma$(k)$ distributed random variable. Let $ X $ be an independent positive random variable with a density that is hyperbolically monotone (HM) of order $ k.$ Then $Y\cdot X$ and $Y/X $ both…
Mixture distributions arise in many application areas, for example as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a…