Related papers: Exchangeable Bernoulli distributions: high dimensi…
The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In…
Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…
Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or…
Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…
The Birnbaum-Saunders distribution is a flexible and useful model which has been used in several fields. In this paper, a new bimodal version of this distribution based on the alpha-skew-normal distribution is established. We discuss some…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…
In statistical network analysis, models for binary adjacency matrices satisfying vertex exchangeability are commonly used. However, such models may fail to capture key features of the data-generating process when interactions, rather than…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
Recently Khmaladze has shown how to `rotate' one empirical process to another. This paper is the first to apply this transform when successive data points are generated by a single distributional family, but with covariates varying over the…
A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the…
In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…