Moment Estimators of the Parameters of Zero-One Inflated Negative Binomial Distribution

In this paper, zero-one inflated negative binomial distribution is considered, along with some of its structural properties, then its parameters were estimated using the method of moments. It is found that the method of moments to estimate the parameters of the zero-one inflated negative binomial models is not a proper method and may give incorrect conclusions.

Authors:

• Rafid Saeed Abdulrazak Alshkaki

Keywords:

• Zero one inflated models
• negative binomial distribution
• moments estimator
• non-negative integer sampling.

References:

[1] Johnson, N. L., Kemp, A. W. and Kotz, S. (2005) Univariate Discrete Distributions, Third Edition, John Wiley and Sons; New Jersey.
[2] 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, 5(2), 292-301.
[3] Saengthong, P., Bodhisuwan, W., and Thongteeraparp, A. (2015). The Zero Inflated Negative Binomial – Crack Distribution: Some Properties And Parameter Estimation. Songklanakarin J. Sci. Technol, 37 (6), 701-711.
[4] Fang, R., Wagner, B. D., Harris, J. K. and Fillon, S. A. (2016). Zero-inflated negative binomial mixed model: an application to two microbial organisms important in oesophagitis. Epidemiology and Infection, 144(11), 2447-2455.
[5] Preisser, J. S., Das, K., Long, D. L. and Divaris, K. (2016). Marginalized zero-inflated negative binomial regression with application to dental caries. Stat Med. 35(10), 1722-35.
[6] Nanjundan, G. and Nika, T. R. (2013). Estimation of the Parameters of the Zero-One Inflated Power Series Distributions, International Journal of Statistika and Mathematika, Vol. 6(3), 109-114.
[7] Banik, S. and Kibria, B. M. G. (2009). On Some Discrete Distributions and their Applications with Real Life Data. Journal of Modern Applied Statistical Methods, 8(2), 423-447.
[8] Alshkaki, R. S. A. (2016). On a Characterization of the Zero-One Inflated Negative Binomial Distribution. Research Journal of Mathematical and Statistical Sciences, Vol. 4(9), 2016, 1-3.