相关论文: On a characterization of exponential and double ex…

The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative L\'evy process \xi with unbounded variation.…

We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted…

A tempered version of the discrete Linnik distribution is introduced in order to obtain integer-valued distribution families connected to stable laws. The proposal constitutes a generalization of the well-known Poisson-Tweedie law, which is…

In this paper introduces a new family of continuous distributions namely the Poison transmuted-G family of distribution is proposed by inducing two addition parameter on the base line G distribution. Some of its mathematical properties…

We characterize the distributions that arise as derivatives of families of probabilities and of positive and signed measures on smooth manifolds.

This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated…

We use sequences which depend on two parameters to define families of ultradifferentiable functions which contain Gevrey classes. It is shown that such families are closed under superposition, and therefore inverse closed as well.…

We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…

The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov…

We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace…

In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information…

We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…

We study power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions. These equations arise when studying distributional equations of the type Z = X + TZ, where T is a known random variable,…

It is well-known that the Shannon entropies of some parameterized probability distributions are concave functions with respect to the parameter. In this paper we consider a family of such distributions (including the binomial, Poisson, and…

Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their…

Semiparametric exponential family proposed by Ning et al. (2017) is an extension of the parametric exponential family to the case with a nonparametric base measure function. Such a distribution family has potential application in some areas…

Compound distributions allow construction of a rich set of distributions. Typically they involve an intractable integral. Here we use a quadrature approximation to that integral to define the quadrature compound family. Special care is…

A quasi-infinitely divisible distribution on $\mathbb{R}$ is a probability distribution whose characteristic function allows a L\'evy-Khintchine type representation with a "signed L\'evy measure", rather than a L\'evy measure.…

Tempered exponential dichotomy formulates the nonuniform hyperbolicity for random dynamical systems. It was described by admissibility of a pair of function classes defined with Lyapunov norms, For MET-systems (systems satisfying the…

The $\lambda$-exponential family generalizes the standard exponential family via a generalized convex duality motivated by optimal transport. It is the constant-curvature analogue of the exponential family from the information-geometric…