Version 1
: Received: 22 March 2021 / Approved: 23 March 2021 / Online: 23 March 2021 (12:57:21 CET)
How to cite:
Tovissodé, C. F.; Glele Kakai, R. A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models. Preprints2021, 2021030570. https://doi.org/10.20944/preprints202103.0570.v1
Tovissodé, C. F.; Glele Kakai, R. A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models. Preprints 2021, 2021030570. https://doi.org/10.20944/preprints202103.0570.v1
Tovissodé, C. F.; Glele Kakai, R. A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models. Preprints2021, 2021030570. https://doi.org/10.20944/preprints202103.0570.v1
APA Style
Tovissodé, C. F., & Glele Kakai, R. (2021). A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models. Preprints. https://doi.org/10.20944/preprints202103.0570.v1
Chicago/Turabian Style
Tovissodé, C. F. and Romain Glele Kakai. 2021 "A Stochastic Condensation Mechanism for Inducing Underdispersion in Count Models" Preprints. https://doi.org/10.20944/preprints202103.0570.v1
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 randomlystopped sums. There is no analogous stochastic mechanism for the construction of underdispersed count variables (variance less than mean), starting from an original count distribution of interest. This work proposes a generic method to stochastically distort an original count variable to obtain a new count variable with relatively less variability than in the original variable. The proposed mechanism, termed condensation, attracts probability masses from the quantiles in the tails of the original distribution and redirect them toward quantiles around the expected value. If the original distribution can be simulated, then the simulation of variates from a condensed distribution is straightforward. Moreover, condensed distributions have a simple mean-parametrization, a characteristic useful in a count regression context. An application to the negative binomial distribution resulted in a distribution allowing under, equi and overdispersion. In addition to graphical insights, fields of applications of special cases of condensed Poisson and condensed negative binomial distributions were pointed out as an indication of the potential of condensation for a flexible analysis of count data
Keywords
Erlang process ; condensed distribution ; probability generating function ; algebraic moments ; Poisson remainder distribution; negative binomial remainder distribution
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.