Related papers: A new over-dispersed count model
The Poisson multinomial distribution (PMD) describes the distribution of the sum of $n$ independent but non-identically distributed random vectors, in which each random vector is of length $m$ with 0/1 valued elements and only one of its…
Modern datasets are characterized by a large number of features that may conceal complex dependency structures. To deal with this type of data, dimensionality reduction techniques are essential. Numerous dimensionality reduction methods…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
Count data are ubiquitous in ecology and the Poisson generalized linear model (GLM) is commonly used to model the association between counts and explanatory variables of interest. When fitting this model to the data, one typically proceeds…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Although its probability mass function (pmf) is known, what is lacking is a $visual$…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…
Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…
This paper proposes a generalized binomial distribution with four parameters, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
Methods used to infer nuclear parameters from neutron count statistics fall into two categories depending on whether they use moments or count number probabilities. As probabilities are in general more difficult to calculate, we are…
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…
The analysis of multivariate discrete data is crucial in various scientific research areas, such as epidemiology, the social sciences, genomics, and environmental studies. As the availability of such data increases, developing robust…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
Consider a graph on randomly scattered points in an arbitrary space, with two points $x,y$ connected with probability $\phi(x,y)$. Suppose the number of points is large but the mean number of isolated points is $O(1)$. We give general…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
The two-parameter Poisson-Dirichlet diffusion takes values in the infinite ordered simplex and extends the celebrated infinitely-many-neutral-alleles model, having a two-parameter Poisson-Dirichlet stationary distribution. Here we identify…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
Many datasets are observed on a finite set of equally spaced directions instead of the exact angles, such as the wind direction data. However, in the statistical literature, bivariate models are only available for continuous circular random…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is…