.svg){kind=logo}
ESTIMATION METHODS FOR THE WEIGHTED POISSON DISTRIBUTION
Keywords:
weighted Poisson distribution, parametric estimation, numerical simulation, real dataDOI:
https://doi.org/10.17654/0972086325005Abstract
In this paper, an underdispersed weighted Poisson distribution is revisited and its statistical and probabilistic properties are introduced and explored. We describe four parametric estimation methods for estimating unknown parameters of the model. Parameter estimation can be used to guide the selection of the best estimation method for the model parameters. This would be very important for reliability engineers and applied statisticians. Numerical simulation experiments are carried out to assess the performance of the estimators obtained. An application is made with real data in order to validate the best method via a Chi-square test of fit.
Received: December 11, 2024
Accepted: February 11, 2025
References
A. A. Al-Babtain, A. M. Gemeay and A. Z. Afify, Estimation methods for the discrete Poisson-Lindley and discrete Lindley distributions with actuarial measures and applications in medicine, Journal of King Saud University-Science 33(2) (2021), 101-224.
H. Al-Mofleh, A. Z. Afify and N. A. Ibrahim, A new extended two-parameter distribution: properties, estimation methods, and applications in medicine and geology, Mathematics 8(9) (2020), 1578.
J. S. Coleman and J. James, The equilibrium size distribution of freely-forming groups, Sociometry 24(1) (1961), 36-45.
J. Del Castillo and M. Perez-Casany, Weighted Poisson distributions for overdispersion and underdispersion situations, Ann. Inst. Statist. Math. 50 (1998), 567-585.
S. Dey, A. Alzaatreh and I. Ghosh, Parameter estimation methods for the Weibull-Pareto distribution, Computational and Mathematical Methods 3(1) (2021), e1053.
M. Ghitany and D. Al-Mutairi, Estimation methods for the discrete Poisson-Lindley distribution, J. Stat. Comput. Simul. 79(1) (2009), 1-9.
A. Henningsen and O. Toomet, maxlik: a package for maximum likelihood estimation in r, Comput. Statist. 26(3) (2011), 443-458.
A. Kiyindou, I. Adoumbaye, D. Mizere and J. Moussa, Influence de la plante-hote sur le developpement et la reproduction de l’aleurode aleurodicus dispersus russell (hom.: Aleyrodidae) en republique du congo, Fruits 54(2) (1999), 115-122.
C. Kokonendji, D. Mizere and N. Balakrishnan, Connections of the Poisson weight function to overdispersion and underdispersion, J. Statist. Plann. Inference 138(5) (2008), 1287-1296.
C. G. Louzayadio, R. O. Malouata and D. M. Koukouatikissa, A weighted Poisson distribution for underdispersed count data, Int. J. Stat. Probab. 10 (2021), 157-165.
G. C. Louzayadio, D. Mizere and R. A. Makany, Estimators comparison of the Poisson canonical parameter and mean dual distributions, Far East Journal of Theoretical Statistics 44(2) (2013), 145-164.
A. Luceno, Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators, Comput. Statist. Data Anal. 51(2) (2006), 904-917.
M. A. Meraou and M. Z. Raqab, Statistical properties and different estimation procedures of Poisson-Lindley distribution, J. Stat. Theory Appl. 20(1) (2021), 33-45.
D. Mizere, Contributions a la modelisation et a l’analyse statistique des donnees de denombrement, Ph.D. Thesis, 2006.
D. Mizere, Modelisation statistique des donnees aleurodicus sur agrume par des lois de poisson ponderees, Afr. Stat. 2(1) (2007), 59-72.
D. Mizere, G. C. Louzayadio, R. Bidounga and G. Kissita, Decomposition d’une loi de poisson ponderee en une combinaison convexe de lois duales, Afrika Statistika 8(1) (2013), 583-594.
G. Patil and C. Rao, Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics 34 (1978), 179-184.
C. R. Rao, On discrete distributions arising out of methods of ascertainment, Sankhya Ser. A 27 (1965), 311-324.
M. S. Ridout and P. Besbeas, An empirical model for underdispersed count data, Stat. Model. 4(1) (2004), 77-89.
G. Shmueli, T. P. Minka, J. B. Kadane, S. Borle and P. Boatwright, A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution, J. Roy. Statist. Soc. Ser. C 54(1) (2005), 127-142.
J. J. Swain, S. Venkatraman and J. R. Wilson, Least-squares estimation of distribution functions in Johnson’s translation system, J. Stat. Comput. Simul. 29(4) (1988), 271-297.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Far East Journal of Theoretical Statistics, 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.
