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In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
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…
Count regression models are necessary for examining discrete dependent variables alongside covariates. Nonetheless, when data display outliers, overdispersion, and an abundance of zeros, traditional methods like the zero-inflated negative…
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…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
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…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
Although models for count data with over-dispersion have been widely considered in the literature, models for under-dispersion -- the opposite phenomenon -- have received less attention as it is only relatively common in particular research…
Accurate modeling is essential in integer-valued real phenomena, including the distribution of entire data, zero-inflated (ZI) data, and discrete exceedances. The Poisson and Negative Binomial distributions, along with their ZI variants,…
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…
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…
There are numerous applications which involve modeling multi-dimensional count data, notably in actuarial science and risk management. When such data exhibit an excess of zeros, common count models are no longer suitable. With multivariate…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
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…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson…
The appropriateness of the Poisson model is frequently challenged when examining spatial count data marked by unbalanced distributions, over-dispersion, or under-dispersion. Moreover, traditional parametric models may inadequately capture…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a…
The potential of location-shift models to find adequate models between the proportional odds model and the non-proportional odds model is investigated. It is demonstrated that these models are very useful in ordinal modeling. While…