Results 21 to 30 of about 212,411 (244)

Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions

Mathematics, 2023
The class of natural exponential families (NEFs) of distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields.
Shaul K. Bar-Lev, Apostolos Batsidis, Jochen Einbeck, Xu Liu, Panpan Ren   +4 more
doaj   +1 more source

Duality for real and multivariate exponential families [PDF]

Journal of Multivariate Analysis, 2021
Consider a measure μ on R generating a natural exponential family F(μ) with variance function VF(μ)(m) and Laplace transform exp(lμ(s)) = ∫ Rn exp(−〈s, x〉)μ(dx). A dual measure μ∗ satisfies −l′ μ∗(−l μ(s)) = s.
G. Letac
semanticscholar   +1 more source

A New Class of Counting Distributions Embedded in the Lee–Carter Model for Mortality Projections: A Bayesian Approach

Risks, 2022
The Lee–Carter model, the dominant mortality projection modeling in the literature, was criticized for its homoscedastic error assumption. This was corrected in extensions to the model based on the assumption that the number of deaths follows Poisson or ...
Yaser Awad, Shaul K. Bar-Lev, Udi Makov
doaj   +1 more source

Deformed Algebras and Generalizations of Independence on Deformed Exponential Families

Entropy, 2015
A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems.
Hiroshi Matsuzoe, Tatsuaki Wada
doaj   +1 more source

Independent, Tough Identical Results: The Class of Tweedie on Power Variance Functions and the Class of Bar-Lev and Enis on Reproducible Natural Exponential Families

International Journal of Statistics and Probability, 2019
The Rao-Blackwell theorem has had a fundamental role in statistical theory. However, as opposed to what seems natural, Rao and Blackwell did not investigate and write the theorem jointly.
S. Bar-Lev
semanticscholar   +1 more source

Group Invariance of Information Geometry on q-Gaussian Distributions Induced by Beta-Divergence

Entropy, 2013
We demonstrate that the q-exponential family particularly admits natural geometrical structures among deformed exponential families. The property is the invariance of structures with respect to a general linear group, which transitively acts on the space
Shinto Eguchi, Atsumi Ohara
doaj   +1 more source

On the Fisher Metric of Conditional Probability Polytopes

Entropy, 2014
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of ...
Guido Montúfar, Johannes Rauh, Nihat Ay
doaj   +1 more source

Piecewise monotone estimation in one-parameter exponential families [PDF]

Statistical Papers, 2021
The problem of estimating a piecewise monotone sequence of normal means is called the nearly isotonic regression. For this problem, an efficient algorithm has been devised by modifying the pool adjacent violators algorithm (PAVA).
T. Matsuda, Y. Miyatake
semanticscholar   +1 more source

Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Measure of Central Tendency

Entropy, 2014
One dimensional exponential families on finite sample spaces are studied using the geometry of the simplex Δn°-1  and that of a transformation Vn-1 of its interior.
Paul Vos, Karim Anaya-Izquierdo
doaj   +1 more source

Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

Entropy, 2016
We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
doaj   +1 more source