相关论文: Estimators, escort probabilities, and phi-exponent…

Many common probability distributions in statistics like the Gaussian, multinomial, Beta or Gamma distributions can be studied under the unified framework of exponential families. In this paper, we prove that both R\'enyi and Tsallis…

Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…

We consider a pair of one-parameter (alpha) families of generalized two-qubit determinantal Hilbert-Schmidt probability distributions, p_{alpha}(|rho^{PT}|) and q_{alpha}(|rho|), where rho is a 4 x 4 density matrix, rho^{PT}, its partial…

Recently much attention has been paid to deep generative models, since they have been used to great success for variational inference, generation of complex data types, and more. In most all of these settings, the goal has been to find a…

For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we…

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that…

We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of…

We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint…

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…

In this report, we explore the data selection leading to a family of estimators maximizing a centrality. The family allows a nice properties leading to accurate and robust probability density function fitting according to some criteria we…

It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…

In this paper, we establish the links between the Lehmer and H\"older mean families and maximum weighted likelihood estimator. Considering the regular one-parameter exponential family of probability density functions, we show that the…

The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds…

We discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption,…

We consider distributed parameter estimation using interactive protocols subject to local information constraints such as bandwidth limitations, local differential privacy, and restricted measurements. We provide a unified framework…

Mixture distributions arise in many parametric and non-parametric settings -- for example, in Gaussian mixture models and in non-parametric estimation. It is often necessary to compute the entropy of a mixture, but, in most cases, this…

We describe a probabilistic methodology, based on random walk estimates, to obtain exponential upper bounds for the probability of observing unusually small maximal components in two classical (near-)critical random graph models. More…

Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer--Rao lower bounds on the…

Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…

Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…