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

@article{Zeviani2014TheGD,
  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},
  year={2014},
  volume={41},
  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
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References

SHOWING 1-10 OF 15 REFERENCES
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.
TLDR
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.
TLDR
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.
TLDR
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.
TLDR
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
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