The zero truncated model is usually used in modeling
count data without zero. It is the opposite of zero inflated model.
Zero truncated Poisson and zero truncated negative binomial models
are discussed and used by some researchers in analyzing the
abundance of rare species and hospital stay. Zero truncated models
are used as the base in developing hurdle models. In this study, we
developed a new model, the zero truncated strict arcsine model,
which can be used as an alternative model in modeling count data
without zero and with extra variation. Two simulated and one real
life data sets are used and fitted into this developed model. The
results show that the model provides a good fit to the data. Maximum
likelihood estimation method is used in estimating the parameters.
<p>[1] G. J. McLachlan, “On the EM algorithm for overdispersed count data,”
Statistical Methods in Medical Research 6, 1997,76-98
[2] J. N. S. Mathews and D. R. Appleton, “An application of the truncated
Poisson distribution to immunogold assay,” Biometrics, 49, 1993, 617-
621.
[3] M. D. Creel andj. B. Loomis, “ Theoretical and empirical advantages of
truncated count data estimators for analysis of deer hunting in
California,” American Journal of Agricultural Economics, 72(2), 1990,
434-441.
[4] A. H. Welsh, R. B. Cunningham, C. G. Donelty, D. B. Lindenmayer,
“Modeling the abundance of rare species: statistical models for counts
with extra zeros”. Ecological Modeling 88, 1996, 297-308.
[5] A. H. Welsh, R. B. Cunningham, R. L. Chambers, “Methodology for
estimating the abundance of rare animals: seabird nesting on north eash
Herald Cay”. Biometrics, 56, 2000, 22-30.
[6] A. H. Lee, k. Wang, K. K. W. Yau and P. J. Somerford, “ Truncated
negative binomial mixed regression modelling of ischaemic stroke
hospitalizations,” Statistics in Medicine, 22, 2003, 1129-1139.
[7] J. T. Grogger and R. T. Carson, ‘ Models for truncated counts.” Journal
of Applied Econometrics, 1991, 6, 225-238.
[8] S. Gurmu, “ Tests for detecting overdispersion in the positive Poisson
regression model,” Journal of the Business and Economic Statistics;
1991,9, 215-222.
[9] J. Kennan, “The duration of contract strikes in U. S. manufacturing,”
Journal of Econometric, 1985, 28, 5-28.
[10] M. E. Ghitany, D. K. Al-mutairi and S. Nadarajah, “ Zero-truncated
Poisson-Lindley distribution an its application,” Mathematics and
Computers in Simulation, 2008, 79, 279-287.
[11] H. H. Thygesen and A. Zwinderman, “Modeling Sage data with a
truncated gamma-Poisson model,” BMC Bioinformatics 2006, 7, 157.
[12] G. Letac and M. Mora, “Natural real exponential families with cubic
variance functions,” The Annals of Statistics, 18, 1990, 1-37.
[13] C. C. Kokonendji and M. Khoudar, “On Strict Arcsine Distribution”
Communications in Statistics. Theory Methods,33(5), 2004, pg993-
1006
[14] W. L. Goffe., G. Ferrier and, J. John Rogers, “Global optimization of
statistical functions with simulated annealing. Journal of Econometric,
60 (1/2), 1994, 65-100.
[15] S. Kirkpatrick, C. D. Gelatt Jr., M. P. Vecchi, "Optimization by
Simulated Annealing",Science, 220, 4598, 671-680, 1983.</p>
<p>[1] G. J. McLachlan, “On the EM algorithm for overdispersed count data,”
Statistical Methods in Medical Research 6, 1997,76-98
[2] J. N. S. Mathews and D. R. Appleton, “An application of the truncated
Poisson distribution to immunogold assay,” Biometrics, 49, 1993, 617-
621.
[3] M. D. Creel andj. B. Loomis, “ Theoretical and empirical advantages of
truncated count data estimators for analysis of deer hunting in
California,” American Journal of Agricultural Economics, 72(2), 1990,
434-441.
[4] A. H. Welsh, R. B. Cunningham, C. G. Donelty, D. B. Lindenmayer,
“Modeling the abundance of rare species: statistical models for counts
with extra zeros”. Ecological Modeling 88, 1996, 297-308.
[5] A. H. Welsh, R. B. Cunningham, R. L. Chambers, “Methodology for
estimating the abundance of rare animals: seabird nesting on north eash
Herald Cay”. Biometrics, 56, 2000, 22-30.
[6] A. H. Lee, k. Wang, K. K. W. Yau and P. J. Somerford, “ Truncated
negative binomial mixed regression modelling of ischaemic stroke
hospitalizations,” Statistics in Medicine, 22, 2003, 1129-1139.
[7] J. T. Grogger and R. T. Carson, ‘ Models for truncated counts.” Journal
of Applied Econometrics, 1991, 6, 225-238.
[8] S. Gurmu, “ Tests for detecting overdispersion in the positive Poisson
regression model,” Journal of the Business and Economic Statistics;
1991,9, 215-222.
[9] J. Kennan, “The duration of contract strikes in U. S. manufacturing,”
Journal of Econometric, 1985, 28, 5-28.
[10] M. E. Ghitany, D. K. Al-mutairi and S. Nadarajah, “ Zero-truncated
Poisson-Lindley distribution an its application,” Mathematics and
Computers in Simulation, 2008, 79, 279-287.
[11] H. H. Thygesen and A. Zwinderman, “Modeling Sage data with a
truncated gamma-Poisson model,” BMC Bioinformatics 2006, 7, 157.
[12] G. Letac and M. Mora, “Natural real exponential families with cubic
variance functions,” The Annals of Statistics, 18, 1990, 1-37.
[13] C. C. Kokonendji and M. Khoudar, “On Strict Arcsine Distribution”
Communications in Statistics. Theory Methods,33(5), 2004, pg993-
1006
[14] W. L. Goffe., G. Ferrier and, J. John Rogers, “Global optimization of
statistical functions with simulated annealing. Journal of Econometric,
60 (1/2), 1994, 65-100.
[15] S. Kirkpatrick, C. D. Gelatt Jr., M. P. Vecchi, "Optimization by
Simulated Annealing",Science, 220, 4598, 671-680, 1983.</p>
@article{"International Journal of Information, Control and Computer Sciences:53048", author = "Y. N. Phang and E. F. Loh", title = "Zero Truncated Strict Arcsine Model", abstract = "The zero truncated model is usually used in modeling
count data without zero. It is the opposite of zero inflated model.
Zero truncated Poisson and zero truncated negative binomial models
are discussed and used by some researchers in analyzing the
abundance of rare species and hospital stay. Zero truncated models
are used as the base in developing hurdle models. In this study, we
developed a new model, the zero truncated strict arcsine model,
which can be used as an alternative model in modeling count data
without zero and with extra variation. Two simulated and one real
life data sets are used and fitted into this developed model. The
results show that the model provides a good fit to the data. Maximum
likelihood estimation method is used in estimating the parameters.
", keywords = "Hurdle models, maximum likelihood estimation
method, positive count data.", volume = "7", number = "7", pages = "901-3", }
