Related papers: Conditional Probabilities of Multivariate Poisson …
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…
This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
We investigate the level spacing distribution for the quantum spectrum of the square billiard. Extending work of Connors--Keating, and Smilansky, we formulate an analog of the Hardy--Littlewood prime $k$-tuple conjecture for sums of two…
This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…
In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
Bayesian Poisson probability distributions for the average n can be analytically converted into equivalent chi-squared distributions. These can then be combined with other Gaussian or Bayesian Poisson distributions to make a total…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…
In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties,…
We consider deep multivariate models for heterogeneous collections of random variables. In the context of computer vision, such collections may e.g. consist of images, segmentations, image attributes, and latent variables. When developing…
Let $(X_1 , \ldots , X_d)$ be random variables taking nonnegative integer values and let $f(z_1, \ldots , z_d)$ be the probability generating function. Suppose that $f$ is real stable; equivalently, suppose that the polarization of this…
Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow…
This paper develops a flexible and computationally efficient multivariate volatility model, which allows for dynamic conditional correlations and volatility spillover effects among financial assets. The new model has desirable properties…
Distribution of the sum of independent identically distributed symmetric lattice vectors is approximated by the accompanying compound Poisson law and the second-order Hipp-type signed compound Poisson measure. Bergstr\"om -type asymptotic…
We introduce and study a multiparameter Poisson process (MPP). In a particular case, it is observed that the MPP has a unique representation. Its subordination with the multivariate subordinator and inverse subordinator are studied in…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
We investigate the variation in the total number of points in a random $p\times p$ square in $\mathbb{Z}^2$ where the $p$-adic valuation of a given polynomial in two variables is precisely $1$. We establish that this quantity follows a…