Estimation of Zero-Inflation Parameter in Zero-Inflated Poisson Model

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2018 by IJMTT Journal
Volume-56 Number-2
Year of Publication : 2018
Authors : K.M.Sakthivel, C.S.Rajitha
  10.14445/22315373/IJMTT-V56P519

MLA

K.M.Sakthivel, C.S.Rajitha "Estimation of Zero-Inflation Parameter in Zero-Inflated Poisson Model", International Journal of Mathematics Trends and Technology (IJMTT). V56(2):135-140 April 2018. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
The modelling of count data is extensively used in many fields of research. There is handful of zero-inflated probability models available in literature. Among these models, zero inflated Poisson distribution is one of the widely used models for modelling data with excess number of zeros. In all the zero-inflated models, one can have parameter called zero-inflation parameter which is in addition to the number of parameters in underlying distribution. The estimation of the zero-inflation parameter of the zero-inflated Poisson (ZIP) models by MLE do not have an explicit expression and solved iteratively by using modern computing techniques. In this paper, we proposed a probability based inflation estimator (PBIE) for making inferences about the inflation parameter of the ZIP model and also studied the performance of the proposed estimator for simulated data.

Reference
[ 1] S. Beckett, J. Jee, T. Ncube, , S. Pompilus, Q.Washington, A. Singh, and N. Pal, “Zero-inflated Poisson (ZIP) distribution: parameter estimation and applications to model data from natural calamities,” Involve: A Journal of Mathematics, vol.7(6),pp. 751–767, 2014.
[2] P.C. Consul, and G.C Jain, “On some interesting properties of the generalized Poisson distribution,” Biometrical Journal, vol. 15, pp. 495–500, 1973b.
[3] F.Famoye, “Parameter estimation for generalized negative binomial distribution,” Communications in Statistics-Simulation and Computation, vol. 26(1), pp. 269–279, 1997
[4] W. Feller, “On a general class of contagious distributions,” Annals of Mathematical Statistics, vol.14 (4), pp.389–400, 1943.
[5] D. Lambert, “Zero-inflated Poisson regression with an application to defects in manufacturing,” Technometrics, vol. 34(1),pp. 1–14, 1992.
[6] G. Nanjundan, and T. R. Naika,. “Asymptotic comparison of method of moments estimators and maximumlikelihood estimators of parameters in zero-inflated poissonmodel,” AppliedMathematics, vol. 3, pp. 610–616, 2012.
[7] J. Neyman, “ On a new class of contagious distributions applicable in entomology and bacteriology,” Annals of Mathematical Statistics, vol. 10(1), pp. 35–57, 1939
[8] M. K. Patil, and D. T. Shirke, “Testing parameter of the power series distribution of a zero-inflated power series model,” Statistical Methodology, vol. 4(4), pp.393–406, 2007.
[9] M. K. Patil, and D. T. Shirke, “Tests for equality of inflation parameters of two zero-inflated power series distributions,” Communications in Statistics-Theory and Methods, vol. 40(14), pp. 2539–2553, 2011.
[10] P. Puig, and J.Valero, “Count data distributions: Some characterizations with applications,” Journal of American Statistical Association, vol. 101(473), pp. 332–340, 2006.
[11] M. Ridout, C.G.B. Demetrio, and J. Hinde, “Models for count data with many zeros,” In International Biometric Conference, Capetown, South Africa, December. 1998
[12] Y. S.Wagh, and K. K. Kamalja, “Comparison of methods of estimation for parameters of Generalized Poisson distribution through simulation study,” Communications in Statistics-Simulation and Computation, vol. 46(5), pp. 4098–4112, 2017.

Keywords
mean squared error, MLE, moment estimators, zero-inflation Parameter, zero-Inflated Poisson Model.