The Gamma-count distribution in the analysis of experimental underdispersed data

  title={The Gamma-count distribution in the analysis of experimental underdispersed data},
  author={W. M. Zeviani and P. J. Ribeiro and W. H. Bonat and S. Shimakura and J. A. Muniz},
  journal={Journal of Applied Statistics},
  pages={2616 - 2626}
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 counts by Gaussian regression models ignores the discreteness, asymmetry and heteroscedasticity and is inefficient, providing unrealistic standard errors or possibly negative predictions of the expected number of events. The Poisson regression is the standard… Expand
A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference
Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting fromExpand
On the Discretization of Continuous Probability Distributions for Flexible Count Regression
Most existing flexible count regression models allow only approximate inference. This 1 work proposes a new framework to provide an exact and flexible alternative for modeling and 2 simulating countExpand
A Weibull-count approach for handling under- and overdispersed longitudinal/clustered data structures
A Weibull-model-based approach is examined to handle under- and overdispersed discrete data in a hierarchical framework. This methodology was first introduced by Nakagawa and Osaki (1975, IEEEExpand
Modelling excess zeros in count data: A new perspective on modelling approaches
We consider models underlying regression analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on twoExpand
Extended Poisson–Tweedie: Properties and regression models for count data
We propose a new class of discrete generalized linear models based on the class of Poisson–Tweedie factorial dispersion models with variance of the form μ + ϕ μ p , where μ is the mean and ϕ and pExpand
Some families of count distributions for modelling zero-inflation and dispersion / Low Yeh Ching
A popular distribution for the modelling of discrete count data is the Poisson distribution. However, count data usually exhibit over dispersion or under dispersion when modelled by a PoissonExpand
Log-linear Conway-Maxwell-Poisson models for dispersed counts
Conway-Maxwell-Poisson (COMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use inExpand
Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts
Conway–Maxwell–Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use inExpand
Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data
The COM–Poisson distribution is a two-parameter generalization of the Poisson distribution that can deal with under-, equi- and overdispersed count data. Unfortunately, its location parameter doesExpand
Double Poisson-Tweedie Regression Models
The results showed that women living out of the capital Curitiba, with viral load equal or larger than 1000 copies and with previous diagnostic of HIV infection, present lower levels of CD4 cell count and the time to initiate the antiretroviral therapy decreases the data dispersion. Expand


Duration dependence and dispersion in count-data models
This paper explores the relation between non-exponential waiting times between events and the distribution of the number of events in a fixed time interval. It is shown that within this framework theExpand
A statistical model for under- or overdispersed clustered and longitudinal count data.
Application of the likelihood-based model to daily counts of asthma inhaler use by children shows substantial within-subject underdispersion, between-subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. Expand
Variance Specification in Event Count Models: From Restrictive Assumptions to a Generalized Estimator
This paper discusses the problem of variance specification in models for event count data. Event counts are dependent variables that can take on only nonnegative integer values, such as the number ofExpand
Count Models Based on Weibull Interarrival Times
The widespread popularity and use of both the Poisson and the negative binomial models for count data arise, in part, from their derivation as the number of arrivals in a given time period assumingExpand
Extension of the application of conway-maxwell-poisson models: analyzing traffic crash data exhibiting underdispersion.
The results of this research show that the COM-Poisson GLM can handle crash data when the modeling output shows signs of underdispersion and that the model proposed in this study provides better statistical performance than the gamma probability and the traditional Poisson models, at least for this data set. Expand
The Gamma-Poisson model as a statistical method to determine if micro-organisms are randomly distributed in a food matrix.
The conclusion of the analysis is that the Gamma-Poisson model distinguishes poorly between variation at the Poisson level and the Gamma level, which means that to determine if data are randomly distributed, i.e., Poisson distributed, the Gamma -Poisson distribution is not a good choice. Expand
Modelling species abundance using the Poisson–Tweedie family
The distribution of an organism species in the environment deviates frequently from randomness due to natural cycles, availability of food resources and avoidance of harm. As a result, observed dataExpand
An empirical model for underdispersed count data
We present a novel distribution for modelling count data that are underdispersed relative to the Poisson distribution. The distribution is a form of weighted Poisson distribution and is shown to haveExpand
Count data models for demographic data.
A generalized event count model is proposed to simultaneously allow for a wide class of count data models and account for over- and underdispersion and is successfully applied to German data on fertility, divorces and mobility. Expand
Characterisation of within-batch and between-batch variability in microbial counts in foods using Poisson-gamma and Poisson-lognormal regression models
Abstract In modelling risk management strategies (i.e., acceptance sampling plans, statistical process control), two basic assumptions have been normally made: that the true concentration ofExpand