On the Zero-One Inflated Poisson Distribution

Rafid Saeed Abdulrazak Alshkaki

doi:doi:10.11648/j.ijsd.20160204.11

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On the Zero-One Inflated Poisson Distribution

Rafid Saeed Abdulrazak Alshkaki

Published in International Journal of Statistical Distributions and Applications (Volume 2, Issue 4)

Received: 18 August 2016 Accepted: 10 September 2016 Published: 10 December 2016

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Abstract

In many sampling involving non negative integer data, the zeros are observed to be significantly higher than the expected assumed model. Such models are called zero-one inflated models. The zero inflated Poisson distribution was recently considered and studied due to its empirical needs and application. In this paper, an extension to the case of zero inflated case is considered, namely, the zero and one inflated Poisson distribution, along with some of its structural properties, and estimation of its parameters using the methods of moments and maximum likelihood estimators were obtained with three empirical examples as well.

Published in	International Journal of Statistical Distributions and Applications (Volume 2, Issue 4)
DOI	10.11648/j.ijsd.20160204.11
Page(s)	42-48
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Poisson Distribution, Zero-One Inflated Model, Maximum Likelihood Estimator, Moments Estimator, Inflated Poisson Distribution

References

[1]	Lambert, D. (1992). Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics, Vol. 34, No. 1, 1-14.
[2]	Van den Broek, J. (1995). A score test for zero inflation in a Poisson distribution, Biometrics Vol. 51, No. 2, 738-743.
[3]	Sharma, H. L. (1987). A Probability Distribution for Out-Migration. Janasamkhya; 5 (2): 95-101.
[4]	Ridout, M., Dem´etrio, C. G. B., and Hinde, J. (1998). Models for count data with many zeros. International Biometric Conference, Cape Town, December 1998.
[5]	Hall, D. B. and Berenhaut, K. S. (2000). Score tests for heterogeneity and overdispersion in zero-inflated Poisson and binomial regression models. The Canadian Journal of Statistics, Vol. 30, No. 3, 415-430.
[6]	Jansakul, N. and Hinde, J. P. (2002). Score tests for Zero- Inflated Poisson Models. Computational Statistics and data Analysis, 40, 75-96.
[7]	Gupta, P. L., Gupta, R. C. and Tripathi, R. C. (2004). Score Test for Zero Inﬂated Generalized Poisson Regression Model. Communications In Statistics, Theory and Methods, Vol. 33, No. 1, 47–64.
[8]	Rodrigues-Motta, M., Gianola, D., Heringstad, B., Rosa, G. J., and Chang, Y. M. (2007). A Zero-Inflated Poisson Model For Genetic Analysis Of The Number Of Mastitis Cases In Norwegian Red Cows. Journal of Dairy Science, 90 (11), 5306-5315.
[9]	Naya, H., Urioste, J. I., Chang, Y., Rodrigues-Motta, Kremer, M. R. and Gianola, D. (2008). A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep. Genetics Selection Evolution 40, 379–394.
[10]	Yang, Z., Hardin, J W., and Addy, C. L. (2009). Testing Overdispersion In The Zero-Inflated Poisson Model. Journal of Statistical Planning and Inference, Volume 139, Issue 9, 3340–3353.
[11]	Hall, D. B. and Shen, J. (2010). Robust Estimation for Zero-Inflated Poisson Regression, Scandinavian Journal of Statistics, Volume 37, Issue 2, 237–252.
[12]	Saffari, S. E. and Adnan, R. (2010). Zero-Inflated Poisson Regression Models with Right Censored Count Data. MATEMATIKA, Volume 27, Number 1, 21–29.
[13]	Momeni, F. (2011). The Generalized Power Series Distributions and their Application. The Journal of Mathematics and Computer Science Vol .2, No. 4, 691-697.
[14]	Kibria, B. M. G., Månsson, K. and Shukur, G. (2011). A Ridge Regression estimator for the zero-inflated Poisson model. CESIS Electronic Working Paper Series, The Royal Institute of technology, Paper No. 257.
[15]	Mouatassim, Y. and Ezzahid, E. H. (2012). Poisson regression and Zero-inflated Poisson regression: application to private health insurance data. European Actuarial Journal, Volume 2, Issue 2, 187–204.
[16]	Sharma, A. K. and Landge, V. S. (2013). Zero Inflated Negative Binomial For Modeling Heavy Vehicle Crash Rate On Indian Rural Highway. International Journal of Advances in Engineering & Technology, Vol. 5, Issue 2, 292-301.
[17]	Gupta, R., Marino, B. S., Cnota, J. F. and Ittenbach, R. F. (2013). Finding The Right Distribution For Highly Skewed Zero-Inflated Clinical Data. Epidemiology Biostatistics and Public Health, Volume 10, Number 1, 1-15.
[18]	Beckett, S., Jee, J., Ncube, T., Pompilus, S., Washington, Q., Singh, A. and Pal, N. (2014). Zero-Inflated Poisson (ZIP) Distribution: Parameter Estimation and Applications to Model Data from Natural Calamities. Involve, Vol. 7, No. 6, 751–767.
[19]	Stewart, P. (2014). A generalized inflated Poisson distribution. (Doctoral dissertation, Marshall University).
[20]	Zhang, C., Tian, G. L., Ng, K. W. (2016). Properties of the Zero-And-One Inflated Poisson Distribution And Likelihood-Based Inference Methods. Statistics And Its Interface, 9(1), 11-32.
[21]	Hassanzadeh, F., & Kazemi, I. (2015). Regression Modeling Of One-Inflated Positive Count Data. Statistical Papers, 1-19.
[22]	Alshkaki, R. S. A. (2016). An Extension to the Zero-Inflated Generalized Power Series Distributions. To be presented at the International Conference on Statistical Distributions and Applications 2016, October 14-16, Niagara Falls, Canada.
[23]	Morgan, B. J. T., Palmer, K. J., and Ridout, M. S. (2007). Negative Score Test Statistics. The American Statistician, Vol. 61, 285–288.

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Rafid Saeed Abdulrazak Alshkaki. (2016). On the Zero-One Inflated Poisson Distribution. International Journal of Statistical Distributions and Applications, 2(4), 42-48. https://doi.org/10.11648/j.ijsd.20160204.11

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ACS Style

Rafid Saeed Abdulrazak Alshkaki. On the Zero-One Inflated Poisson Distribution. Int. J. Stat. Distrib. Appl. 2016, 2(4), 42-48. doi: 10.11648/j.ijsd.20160204.11

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AMA Style

Rafid Saeed Abdulrazak Alshkaki. On the Zero-One Inflated Poisson Distribution. Int J Stat Distrib Appl. 2016;2(4):42-48. doi: 10.11648/j.ijsd.20160204.11

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@article{10.11648/j.ijsd.20160204.11,
  author = {Rafid Saeed Abdulrazak Alshkaki},
  title = {On the Zero-One Inflated Poisson Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {2},
  number = {4},
  pages = {42-48},
  doi = {10.11648/j.ijsd.20160204.11},
  url = {https://doi.org/10.11648/j.ijsd.20160204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160204.11},
  abstract = {In many sampling involving non negative integer data, the zeros are observed to be significantly higher than the expected assumed model. Such models are called zero-one inflated models. The zero inflated Poisson distribution was recently considered and studied due to its empirical needs and application. In this paper, an extension to the case of zero inflated case is considered, namely, the zero and one inflated Poisson distribution, along with some of its structural properties, and estimation of its parameters using the methods of moments and maximum likelihood estimators were obtained with three empirical examples as well.},
 year = {2016}
}

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TY  - JOUR
T1  - On the Zero-One Inflated Poisson Distribution
AU  - Rafid Saeed Abdulrazak Alshkaki
Y1  - 2016/12/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ijsd.20160204.11
DO  - 10.11648/j.ijsd.20160204.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 42
EP  - 48
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20160204.11
AB  - In many sampling involving non negative integer data, the zeros are observed to be significantly higher than the expected assumed model. Such models are called zero-one inflated models. The zero inflated Poisson distribution was recently considered and studied due to its empirical needs and application. In this paper, an extension to the case of zero inflated case is considered, namely, the zero and one inflated Poisson distribution, along with some of its structural properties, and estimation of its parameters using the methods of moments and maximum likelihood estimators were obtained with three empirical examples as well.
VL  - 2
IS  - 4
ER  -

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Author Information

Rafid Saeed Abdulrazak Alshkaki

General Requirements Department, Ahmed Bin Mohammed Military College, Doha, Qatar

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Rafid Saeed Abdulrazak Alshkaki. (2016). On the Zero-One Inflated Poisson Distribution. International Journal of Statistical Distributions and Applications, 2(4), 42-48. https://doi.org/10.11648/j.ijsd.20160204.11

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ACS Style

Rafid Saeed Abdulrazak Alshkaki. On the Zero-One Inflated Poisson Distribution. Int. J. Stat. Distrib. Appl. 2016, 2(4), 42-48. doi: 10.11648/j.ijsd.20160204.11

Copy | Download

AMA Style

Rafid Saeed Abdulrazak Alshkaki. On the Zero-One Inflated Poisson Distribution. Int J Stat Distrib Appl. 2016;2(4):42-48. doi: 10.11648/j.ijsd.20160204.11

Copy | Download

@article{10.11648/j.ijsd.20160204.11,
  author = {Rafid Saeed Abdulrazak Alshkaki},
  title = {On the Zero-One Inflated Poisson Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {2},
  number = {4},
  pages = {42-48},
  doi = {10.11648/j.ijsd.20160204.11},
  url = {https://doi.org/10.11648/j.ijsd.20160204.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160204.11},
  abstract = {In many sampling involving non negative integer data, the zeros are observed to be significantly higher than the expected assumed model. Such models are called zero-one inflated models. The zero inflated Poisson distribution was recently considered and studied due to its empirical needs and application. In this paper, an extension to the case of zero inflated case is considered, namely, the zero and one inflated Poisson distribution, along with some of its structural properties, and estimation of its parameters using the methods of moments and maximum likelihood estimators were obtained with three empirical examples as well.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - On the Zero-One Inflated Poisson Distribution
AU  - Rafid Saeed Abdulrazak Alshkaki
Y1  - 2016/12/10
PY  - 2016
N1  - https://doi.org/10.11648/j.ijsd.20160204.11
DO  - 10.11648/j.ijsd.20160204.11
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 42
EP  - 48
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20160204.11
AB  - In many sampling involving non negative integer data, the zeros are observed to be significantly higher than the expected assumed model. Such models are called zero-one inflated models. The zero inflated Poisson distribution was recently considered and studied due to its empirical needs and application. In this paper, an extension to the case of zero inflated case is considered, namely, the zero and one inflated Poisson distribution, along with some of its structural properties, and estimation of its parameters using the methods of moments and maximum likelihood estimators were obtained with three empirical examples as well.
VL  - 2
IS  - 4
ER  -

Copy | Download