Related papers: On count data models based on Bernstein functions …
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data, with sparsity exhibited by an over-abundance of zeros and small non-zero counts. Existing approaches for analyzing multivariate…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical…
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the…
In this paper we introduce and study the class of multivariate strong and strongly subexponential distributions. Some first properties are verified, as for example a type of multivariate analogue of Kesten's inequality, the closure property…
Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of…
Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…
We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative…
We investigate the Conway--Maxwell multivariate Bernoulli distributions, a family of multivariate Bernoulli distributions derived from the Conway--Maxwell-binomial distribution. We show that it is possible to set the parametrization such…
We introduce a nonasymptotic framework for sub-Poisson distributions with moment generating function dominated by that of a Poisson distribution. At its core is a new notion of optimal sub-Poisson variance proxy, analogous to the variance…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
A concentration result for quadratic form of independent subgaussian random variables is derived. If the moments of the random variables satisfy a "Bernstein condition", then the variance term of the Hanson-Wright inequality can be…
We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
Diffusion models have excelled at generative tasks for both continuous and token-based domains, but their application to discrete ordinal data remains underdeveloped. We present CountsDiff, a diffusion framework designed to natively model…
Bivariate count models having one marginal and the other conditionals being of the Poissons form are called pseudo-Poisson distributions. Such models have simple exible dependence structures, possess fast computation algorithms and generate…
Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are…
Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…