On Variance Estimation for the Population Size Estimator under One-Inflated Positive Poisson Distribution
DOI:
https://doi.org/10.11113/mjfas.v18n2.2372Keywords:
Horvitz-Thompson estimator, capture-recapture, count inflation, zero-truncated PoissonAbstract
Let NO1PPbe the Horvitz-Thompson estimator for the population size with one-inflated positive Poisson distribution as the underlying distribution. We estimate the variance of this estimator using conditional expectation technique and provide some descriptions on the variance and its associated confidence interval based on simulation study and real data applications.
References
R. Godwin and D. Böhning, “Estimation of the population size by using the one-inflated positive Poisson model,” Journal of the Royal Statistical Society, Series C (Applied Statistics), vol. 66, no. 2, pp. 425-448, 2017.
D. G. Horvitz and D. J. Thompson, “A generalization of sampling without replacement from a finite universe,” Journal of the American Statistical Association, vol. 47, no. 260, pp. 663-685, 1952.
D. Böhning, “A simple variance formula for population size estimators by conditioning,” Statistical Methodology, vol. 5, no. 5, pp. 410-423, 2008.
R. R. M. Tajuddin, N. Ismail and K. Ibrahim, “Comparison of estimation methods for one-inflated positive Poisson distribution,” Journal of Taibah University for Science, vol. 15, no. 1, pp. 869-881, 2021.
F. N. David and N. L. Johnson, “The truncated Poisson,” Biometrics, vol. 8, no. 4, pp. 275-285, 1952.
O. Anan, D. Böhning and A. Maruotti, “Population size estimation and heterogeneity in capture-recapture data: a linear regression estimator based on the Conway-Maxwell-Poisson distribution,” Statistical Methods & Applications, vol. 26, no. 1, pp. 49-79, 2016.
O. Anan, D. Böhning and A. Maruotti, “On the Turing estimator in capture-recapture count data under the geometric distribution,” Metrika, vol. 82, no. 2, pp. 149-172, 2019.
D. Böhning, P. Kaskasamkul and P. G. M. Van der Heijden, “A modification of Chao’s lower bound estimator in the case of one-inflation,” Metrika, vol. 82, no. 3, pp. 361-384, 2019.
R. R. M. Tajuddin, N. Ismail and K. Ibrahim, “Estimating population size of criminals: a new Horvitz–Thompson estimator under one-inflated positive Poisson-Lindley model,” Crime and Delinquency, 2021.
G. Casella and R. L. Berger, “Statistical inference (2nd edition)”, Duxbury Press, Belmont, 2002.
D. J. Finney and G. C. Varley, “An example of the truncated Poisson distribution,” Biometrics, vol. 11, no. 3, pp. 387-394, 1955.
P. G. M. Van der Heijden, R. Bustami, M. J. Cruyff, G. Engbersen and H. C. Van Houwelingen, “Point and interval estimation of the population size using the truncated Poisson regression model,” Statistical Modelling, vol. 3, no. 4, 305-322, 2003.
D. Böhning and P. G. M. Van der Heijden, “The identity of the zero-truncated, one-inflated likelihood and the zero-one-truncated likelihood for general count densities with an application to drink-driving in Britain,” The Annals of Applied Statistics, vol. 13, no. 2, 1198-1211, 2019.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Razik Ridzuan Mohd Tajuddin, Noriszura Ismail, Noriszura Ismail, Kamarulzaman Ibrahim, Kamarulzaman Ibrahim
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.