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Related papers: Jensen divergence based on Fisher's information

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Given a probability measure with density, Fermat distances and density-driven metrics are conformal transformations of the Euclidean metric that shrink distances in high density areas and enlarge distances in low density areas. Although…

Statistics Theory · Mathematics 2026-01-22 Jérôme Taupin , Frédéric Chazal

Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced…

Statistics Theory · Mathematics 2007-06-13 Fumiyasu Komaki

R\'enyi divergence is related to R\'enyi entropy much like information divergence (also called Kullback-Leibler divergence or relative entropy) is related to Shannon's entropy, and comes up in many settings. It was introduced by R\'enyi as…

Information Theory · Computer Science 2010-05-28 Tim van Erven , Peter Harremoës

The Cramer-Rao product of the Fisher information and the variance of a probability density \rho(x), defined on a domain \Delta \in R^D, is found to have a minimum value reached by the density associated with the ground state of the harmonic…

Mathematical Physics · Physics 2010-01-20 J. S. Dehesa , A. R. Plastino , P. Sanchez-Moreno , C. Vignat

Since its introduction in 1950, Fisher's dispersion test has become a standard means of deciding whether or not count data follow the Poisson distribution. The test is based on a characteristic property of the Poisson distribution, and…

Applications · Statistics 2025-03-21 Erekle Khurodze , Leigh A Roberts

Uncertain input of a mathematical model induces uncertainties in the output and probabilistic sensitivity analysis identifies the influential inputs to guide decision-making. Of practical concern is the probability that the output would, or…

Information Theory · Computer Science 2022-07-12 Jiannan Yang

Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the…

Quantum Physics · Physics 2015-04-20 Angelo Plastino , Guido Bellomo , Angel R. Plastino

If the probability distribution model aims to approximate the hidden mother distribution, it is imperative to establish a useful criterion for the resemblance between the mother and the model distributions. This study proposes a criterion…

Statistics Theory · Mathematics 2025-11-13 Yo Sheena

A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…

Methodology · Statistics 2024-07-02 Qingyang Liu , Xianzheng Huang , Haiming Zhou

We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…

Statistical Mechanics · Physics 2008-12-10 Raymond J. Hawkins , B. Roy Frieden

For a given metric $g_{\mu\nu}$, which is identified as Fisher information metric, we generate new constraints for the probability distributions for physical systems. We postulate the existence of intrinsic probability distributions for…

Quantum Physics · Physics 2014-12-25 Tzu-Chao Hung

A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the…

Statistical Mechanics · Physics 2015-05-13 Takuya Yamano

A new information-theoretic approach to the central limit theorem for stable laws is presented. The main novelty is the concept of relative fractional Fisher information, which shares most of the properties of the classical one, included…

Information Theory · Computer Science 2015-04-28 Giuseppe Toscani

We investigate behavior of the Fisher information matrix of general stable distributions. DuMouchel (1975, 1983) proved that the Fisher information of characteristic exponent \alpha diverges to infinity as \alpha approaches 2. Nagaev and…

Statistics Theory · Mathematics 2007-06-13 Muneya Matsui

The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…

Computation · Statistics 2016-02-17 Omri Har Shemesh , Rick Quax , Borja Miñano , Alfons G. Hoekstra , Peter M. A. Sloot

A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…

Information Theory · Computer Science 2018-02-14 Alan Wisler , Visar Berisha , Andreas Spanias , Alfred O. Hero

This article introduces two new measures for authorship attribution - Rank-Turbulence Delta and Jensen-Shannon Delta - which generalise Burrows's classical Delta by applying distance functions designed for probabilistic distributions. We…

Computation and Language · Computer Science 2026-05-27 Dmitry Pronin , Evgeny Kazartsev

An important aspect of the shape of a distribution is the level of asymmetry. Strong asymmetries play a role in many ecosystems and are found in the size and reproductive success of individuals. But the standard third moment coefficient of…

Methodology · Statistics 2022-09-23 Mario Schlemmer

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a…

Information Theory · Computer Science 2015-04-14 Frank Lad , Giuseppe Sanfilippo , Gianna Agrò

In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…

Statistics Theory · Mathematics 2008-08-22 Alessandro De Gregorio , Stefano Iacus