Results 1 to 10 of about 54,605 (153)

Natural Gradient Flow in the Mixture Geometry of a Discrete Exponential Family [PDF]

Entropy, 2015
In this paper, we study Amari’s natural gradient flows of real functions defined on the densities belonging to an exponential family on a finite sample space.
Luigi Malagò, Giovanni Pistone
doaj   +6 more sources

Natural Exponential Families with Quadratic Variance Functions

Annals of Statistics, 1982
The normal, Poisson, gamma, binomial, and negative binomial distributions are univariate natural exponential families with quadratic variance functions (the variance is at most a quadratic function of the mean). Only one other such family exists. Much theory is unified for these six natural exponential families by appeal to their quadratic variance ...
Carl N Morris
exaly   +3 more sources

A new variance estimation in natural exponential families

Research in Statistics
This article focuses on improving the estimation of population variances for natural exponential family distributions, drawing inspiration from the innovative idea presented by Stein.
Arampamoorthy Laheetharan, Nalini Satkunanathan   +1 more
doaj   +2 more sources

The Exponential Dispersion Model Generated by the Landau Distribution—A Comprehensive Review and Further Developments

Mathematics, 2023
The paper comprehensively studies the natural exponential family and its associated exponential dispersion model generated by the Landau distribution. These families exhibit probabilistic and statistical properties and are suitable for modeling skewed ...
Shaul K. Bar-Lev
doaj   +1 more source

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

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

The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk

Mathematics, 2022
The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the ...
Shaul K. Bar-Lev, Ad Ridder
doaj   +1 more source

Exponential Families with External Parameters

Entropy, 2022
In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters.
Marco Favretti
doaj   +1 more source

Rényi Cross-Entropy Measures for Common Distributions and Processes with Memory

Entropy, 2022
Two Rényi-type generalizations of the Shannon cross-entropy, the Rényi cross-entropy and the Natural Rényi cross-entropy, were recently used as loss functions for the improved design of deep learning generative adversarial networks.
Ferenc Cole Thierrin, Fady Alajaji, Tamás Linder   +2 more
doaj   +1 more source

Quasi-monomials with respect to subgroups of the plane affine group

Математичні Студії, 2023
Let $H$ be a subgroup of the plane affine group ${\rm Aff}(2)$ considered with the natural action on the vector space of two-variable polynomials. The polynomial family $\{ B_{m,n}(x,y) \}$ is called quasi-monomial with respect to $H$ if the group ...
N. M. Samaruk
doaj   +1 more source