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This paper introduces the Generalized Fractional Compound Poisson Process (GFCPP), which claims to be a unified fractional version of the compound Poisson process (CPP) that encompasses existing variations as special cases. We derive its…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
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…
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…
Non-negative matrix factorization (NMF) is widely used as a feature extraction technique for matrices with non-negative entries, such as image data, purchase histories, and other types of count data. In NMF, a non-negative matrix is…
Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an…
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…
At the present time reliably established that probability density functions of gene expression of microarray experiments possess a number of universal properties. First of all these distributions have power asymptotic and secondly the shape…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely…
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…
A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…
Models such as the zero-inflated and zero-altered Poisson and zero-truncated binomial are well-established in modern regression analysis. We propose a super model that jointly and maximally unifies alteration, inflation, truncation and…
The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
Multi-dimensional data frequently occur in many different fields, including risk management, insurance, biology, environmental sciences, and many more. In analyzing multivariate data, it is imperative that the underlying modelling…
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…
By discussing several examples, the theory of generalized functional models is shown to be very natural for modeling some situations of reasoning under uncertainty. A generalized functional model is a pair (f, P) where f is a function…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…