A generalized stochastic condensation mechanism for inducing underdispersion in count models

Abstract

It is quite easy to stochastically distort an original count variable to obtain a new count variable with relatively more variability than in the original variable. Many popular overdispersion models (variance greater than mean) can indeed be obtained by mixtures, compounding or randomly stopped sums. This work proposes a stochastic mechanism, termed generalized condensation, for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. For illustrative purposes, we developed the generalized condensed Poisson distribution, which allows for both under- and equidispersion. An application on a dataset demonstrates the potential of the proposal to accommodate underdispersion in the analysis of real count data.

Keywords:

• Morse-Jewel distribution
• condensed Poisson distribution
• distribution functions
• algebraic moments
• Poisson remainder distribution

Acknowledgments

The authors would like to thank the Associate Editor and an anonymous reviewer for their careful reading of the different versions of the manuscript and insightful suggestions. The authors are also grateful to Robinah Nalwanga for providing language help.

Disclosure statement

The authors declare that there is no conflict of interest(s).