相关论文: On a characterization of exponential and double ex…
This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped).…
It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the…
A new class of distributions, called Generalized One Parameter Polynomial Exponential-G family of distributions is proposed for modelling lifetime data. An account of the structural and reliability properties of the new class is presented.…
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are…
We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…
The exponential family is well known in machine learning and statistical physics as the maximum entropy distribution subject to a set of observed constraints, while the geometric mixture path is common in MCMC methods such as annealed…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power…
Consider a measure $\mu$ on $\R^n$ generating a natural exponential family $F(\mu)$ with variance function $V_{F(\mu)}(m)$ and Laplace transform $$ \exp(\ell_{\mu}(s))=\int_{\R^n} \exp(-\<s,x\>)\mu(dx).$$ A dual measure $\mu^*$ satisfies…
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea of obtaining such densities is firstly to build some…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…
Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description of certain effects of finiteness of statistical systems, in…
In this paper, three different proofs to a result of Wang, Peng and Yang (2013) which related to the joint mixability of elliptical distributions with the same characteristic generator are present. Moreover, we generalize this result to any…
We construct new tests of exponentiality based on Yanev-Chakraborty's characterization of exponential law. We calculate limiting distributions of new tests, local Bahadur efficiency for common alternatives and describe conditions of their…
We establish exponential inequalities for a class of V-statistics under strong mixing conditions. Our theory is developed via a novel kernel expansion based on random Fourier features and the use of a probabilistic method. This type of…
An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity…
In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by…
In this paper, we introduce a new class of bivariate distributions called the bivariate exponentiated extended Weibull distributions. The model introduced here is of Marshall-Olkin type. This new class of bivariate distributions contains…