相关论文: Some incomplete and boundedly complete families of…
We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
We show that maximal families of mutually unbiased bases are characterized in all dimensions by partitioned unitary error bases, up to a choice of a family of Hadamards. Furthermore, we give a new construction of partitioned unitary error…
The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We present \textit{universal} estimators for the statistical mean, variance, and scale (in particular, the interquartile range) under pure differential privacy. These estimators are universal in the sense that they work on an arbitrary,…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…
We consider three new classes of exponential dispersion models of discrete probability distributions which are defined by specifying their variance functions in their mean value parameterization. In a previous paper (Bar-Lev and Ridder,…
We present a novel approach to estimating discrete distributions with (potentially) infinite support in the total variation metric. In a departure from the established paradigm, we make no structural assumptions whatsoever on the sampling…
A series of detailed quantitative results is established for the family of demi-distributions which is a large extension of the family of usual distributions.
For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $\theta$ for cases where $\theta > 0$, extending an earlier result of \cite{voinov1985unbiased} applicable to a…
We show that certain families of sets in $\mathbb{R}^2$ (or $\mathbb{R}^n$) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately definable in the real field, an o-minimal structure.
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
Using the technique developed in approximation theory, we construct examples of exponential families of infinitely divisible laws which can be viewed as deformations of the normal, gamma, and Poisson exponential families. Replacing the…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
We discuss a class of binary parametric families with conditional probabilities taking the form of generalized linear models and show that this approach allows to model high-dimensional random binary vectors with arbitrary mean and…