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Related papers: Extended Poisson INAR(1) processes with equidisper…

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We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

Statistics Theory · Mathematics 2014-09-29 Bent Jørgensen , Célestin C. Kokonendji

Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…

Probability · Mathematics 2025-09-01 Nicolas Lanchier

Event counts are response variables with non-negative integer values representing the number of times that an event occurs within a fixed domain such as a time interval, a geographical area or a cell of a contingency table. Analysis of…

In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…

Methodology · Statistics 2024-12-16 Nicolas Baradel

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…

Numerical Analysis · Mathematics 2019-09-04 Chen Zhang , Simon Arridge , Bangti Jin

We suggest a new hardcore Poisson-type distribution for Young diagrams with the row lengths from some finite list. A discrete variant of the time-ordered Mat\'{e}rn II process in 1D is employed. This approach is related to that based on the…

Combinatorics · Mathematics 2022-06-17 Ivan Cherednik

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-,…

Although many time series are realizations from discrete processes, it is often that a continuous Gaussian model is implemented for modeling and forecasting the data, resulting in incoherent forecasts. Forecasts using a Poisson-Lindley…

Methodology · Statistics 2024-05-31 Rachel D. Gidaro , Jane L. Harvill

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from…

Methodology · Statistics 2013-10-08 Antonio Canale , David B. Dunson

Count-weighted temporal networks often exhibit unequal dispersion in the edge weights, which cannot be fully explained by modelling observational heterogeneity through latent factors in the conditional mean. Therefore, we propose new…

Methodology · Statistics 2026-04-15 Giulia Carallo , Roberto Casarin , Antonio Peruzzi

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…

Probability · Mathematics 2016-02-09 Yi-Ching Yao , Daniel Wei-Chung Miao , Xenos Chang-Shuo Lin

In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the…

Methodology · Statistics 2019-03-01 Johannes Bracher

INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling…

Methodology · Statistics 2020-04-21 Matheus B. Guerrero , Wagner Barreto-Souza , Hernando Ombao

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…

Methodology · Statistics 2016-04-15 Jyotishka Datta , David B. Dunson

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.…

Methodology · Statistics 2008-09-08 Stanley Xu , Gary Grunwald , Richard Jones

Modeling spatial overdispersion requires point processes models with finite dimensional distributions that are overdisperse relative to the Poisson. Fitting such models usually heavily relies on the properties of stationarity, ergodicity,…

Probability · Mathematics 2018-01-12 Mimoza Zografi , Evdokia Xekalaki

We present a new modelling approach for longitudinal count data that is motivated by the increasing availability of longitudinal RNA-sequencing experiments. The distribution of RNA-seq counts typically exhibits overdispersion,…

Methodology · Statistics 2020-08-27 Mirko Signorelli , Pietro Spitali , Roula Tsonaka

This work consists in the asymptotic analysis of the solution of Poisson equation in a bounded domain of $\mathbb{R}^{P}$ $(P=2,3)$ with a thin layer. We use a method based on hierarchical variational equations to derive asymptotic…

Analysis of PDEs · Mathematics 2014-01-14 Khaled El-Ghaouti Boutarene

This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and…

Methodology · Statistics 2020-02-12 Giulia Carallo , Roberto Casarin , Christian P. Robert

A new integer--valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. This process family provides a flexible modelling framework for count data, allowing for under and over--dispersion,…

Methodology · Statistics 2024-12-18 Ovielt Baltodano Lopez , Federico Bassetti , Giulia Carallo , Roberto Casarin