Related papers: Splitting models for multivariate count data
The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete…
Constraint problems can be trivially solved in parallel by exploring different branches of the search tree concurrently. Previous approaches have focused on implementing this functionality in the solver, more or less transparently to the…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
In this note, we provide a refined analysis of Mitra's algorithm \cite{mitra2008clustering} for classifying general discrete mixture distribution models. Built upon spectral clustering \cite{mcsherry2001spectral}, this algorithm offers…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
Much work has been done in the area of the cluster weighted model (CWM), which extends the finite mixture of regression model to include modelling of the covariates. Although many types of distributions have been considered for both the…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…
A main difficulty in actuarial claim size modeling is that there is no simple off-the-shelf distribution that simultaneously provides a good distributional model for the main body and the tail of the data. In particular, covariates may have…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively,…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
The rapid emergence of massive datasets in various fields poses a serious challenge to traditional statistical methods. Meanwhile, it provides opportunities for researchers to develop novel algorithms. Inspired by the idea of…