A REVIEW OF BIVARIATE COM-POISSON DISTRIBUTIONS INTO TYPE 1, TYPE 2 AND TYPE 3 MODELS
Keywords:
univariate COM-Poisson distribution, bivariate COM-Poisson distributionDOI:
https://doi.org/10.17654/0972086324014Abstract
This paper reviews bivariate COM-Poisson laws as the type 1, type 2 and type 3 models. The COM-Poisson distributions of type 1, type 2 and type 3 are shown to be members of the family of bivariate Poisson distributions. Functional relationships among them are also established.
Received: March 28, 2024
Revised: April 29, 2024
Accepted: May 9, 2024
References
P. C. Batsindila Nganga, R. Bidounga and D. Mizère, The covariance structure of the bivariate weighted Poisson distribution and application to the Aleurodicus data, Afrika Statistika 14(2) (2019), 1999-2017.
P. Berkhout and E. Plug, A bivariate count data model using conditional probabilities, Statist. Neerlandica 58(3) (2004), 349-364.
R. Bidounga, E. G. B. Mandangui Maloumbi, R. F. Mizélé Kitoti and D. Mizère, The new bivariate Conway-Maxwell-Poisson distribution obtained by crossing method, International Journal of Statistics and Probability 9(6) (2020), 7032-7040.
R. Bidounga, P. C. Batsindila Nganga, L. Niéré and D. Mizère, A note on the (weighted) bivariate Poisson distribution, European Journal of Pure and Applied Mathematics 14(1) (2021), 192-203.
R. Bidounga, M. Koukouatikissa Diafouka, R. F. Mizélé Kitoti and D. Mizère, The bivariate extended Poisson distribution of type 1, European Journal of Pure and Applied Mathematics 14(4) (2021), 1517 1520.
R. W. Conway and W. L. Maxwell, A queuing model with state dependent service rates, J. Ind. Eng. 12 (1962), 132-136.
L. L. Elion, M. Koukouatikissa Diafouka, R. Bidounga, C. G. Louzayadio, D. Mizèee, R. Makany and G. Kissita, The bivariate weighted Poisson distribution: Statistical study of arterial hypertension data according to the blood sugar level, Far East Journal of Theoretical Statistics 52(5) (2016), 365 393.
P. Holgate, Estimation for the bivariate Poisson distribution, Biometrika 51 (1964), 241-245.
Kimberly F. Sellers, The Conway-Maxwell-Poisson Distribution, Cambridge University Press, 2023.
C. C. Kokonendji, D. Mizère and N. Balakrishnan, Connections of the Poisson weight function to overdispersion and underdispersion, Journal of Statistical Planning and Inference 138 (2008), 1287-1296.
J. Lakshminarayana, S. N. N. Pandit and K. Srinivasa Rao, On a bivariate Poisson distribution, Communication in Statistics Theory and Methods 28(2) (1999), 267 276.
C. G. Louzayadio, E. Nguessolta, M. Koukouatikissa Diafouka and D. Mizère, The bivariate extended Poisson distribution of type 2, Journal of Computer Sciences and Applied Mathematics 5(2) (2023), 89-102.
S. H. Ong, R. C. Gupta, T. Ma and S. Z. Sim, Bivariate Conway-Maxwell Poisson distribution with given marginals and correlation, Journal of Statistical Theory and Practice 15 (2021), 10.
I. O. Sarmanov, Generalized normal correlation and two dimensional Frechet classes, Soviet Math Doki 7 : 596-599, English translation; Russian original in Doki. Akad. Nauk. SSSR 168 (1966), 33-35.
G. Shmueli, T. P. Minka, J. B. Kadane, S. Borle and P. Boatwright, A useful distribution for fitting discrete data: Revival of Conway-Maxwell-Poisson distribution, Appl. Stat. 54(1) (2005), 127-142.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.






