Modeling data with a truncated and inflated Poisson distribution

Modeling data with a truncated and inflated Poisson distribution Zero inflated Poisson regression is a model commonly used to analyze data with excessive zeros. Although many models have been developed to fit zero-inflated data, most of them strongly depend on the special features of the individual data. For example, there is a need for new models when dealing with truncated and inflated data. In this paper, we propose a new model that is sufficiently flexible to model inflation and truncation simultaneously, and which is a mixture of a multinomial logistic and a truncated Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts. The truncated Poisson regression models the counts that are assumed to follow a truncated Poisson distribution. The performance of our proposed model is evaluated through simulation studies, and our model is found to have the smallest mean absolute error and best model fit. In the empirical example, the data are truncated with inflated values of zero and fourteen, and the results show that our model has a better fit than the other competing models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistical Methods & Applications Springer Journals

Modeling data with a truncated and inflated Poisson distribution

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Statistics; Statistics, general; Statistical Theory and Methods
ISSN
1618-2510
eISSN
1613-981X
D.O.I.
10.1007/s10260-017-0377-z
Publisher site
See Article on Publisher Site

Abstract

Zero inflated Poisson regression is a model commonly used to analyze data with excessive zeros. Although many models have been developed to fit zero-inflated data, most of them strongly depend on the special features of the individual data. For example, there is a need for new models when dealing with truncated and inflated data. In this paper, we propose a new model that is sufficiently flexible to model inflation and truncation simultaneously, and which is a mixture of a multinomial logistic and a truncated Poisson regression, in which the multinomial logistic component models the occurrence of excessive counts. The truncated Poisson regression models the counts that are assumed to follow a truncated Poisson distribution. The performance of our proposed model is evaluated through simulation studies, and our model is found to have the smallest mean absolute error and best model fit. In the empirical example, the data are truncated with inflated values of zero and fourteen, and the results show that our model has a better fit than the other competing models.

Journal

Statistical Methods & ApplicationsSpringer Journals

Published: Mar 17, 2017

References

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