Related papers: Exchangeable Bernoulli distributions: high dimensi…
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 use the geometric concept of principal angles between subspaces to compute the noncommutative distribution of an expression involving two free projections. For example, this allows to simplify a formula by…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
Inter-relations between random matrix ensembles with different symmetry types provide inter-relations between generating functions for the gap probabilites at the spectrum edge. Combining these in the scaled limit with the exact evaluation…
This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.
In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.
The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…
The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing…
The negative binomial distribution has been widely used as a more flexible model than the Poisson distribution for count data. However, when the true data-generating process is Poisson, it is often challenging to distinguish it from a…
We consider fixed-point equations for probability distributions on isometry classes of measured metric spaces. The construction is required to be recursive and tree-like, but we allow loops for the geodesics between points in the support of…
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…
Azzalini (1985) introduced a skew-normal distribution of which normal distribution is a special case. Recently Kundu (2014) introduced a geometric skew-normal distribution and showed that it has certain advantages over Azzalini's…