Related papers: New exponential dispersion models for count data -…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…
In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…
In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have…
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
We study the effects of missingness on the estimation of population parameters. Moving beyond restrictive missing completely at random (MCAR) assumptions, we first formulate a missing data analogue of Huber's arbitrary…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
Random graphs, where the connections between nodes are considered random variables, have wide applicability in the social sciences. Exponential-family Random Graph Models (ERGM) have shown themselves to be a useful class of models for…
Overdispersed count data are modelled with likelihood and non-likelihood approaches. Likelihood approaches include the Poisson mixtures with three distributions, the gamma, the lognormal, and the inverse Gaussian distributions.…
We introduce marginalization models (MAMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling by explicitly modeling all induced marginal distributions.…
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…
Generative models have shown strong generation ability while efficient likelihood estimation is less explored. Energy-based models~(EBMs) define a flexible energy function to parameterize unnormalized densities efficiently but are notorious…
Poisson regression is a popular tool for modeling count data and is applied in a vast array of applications from the social to the physical sciences and beyond. Real data, however, are often over- or under-dispersed and, thus, not conducive…
Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…