ON MODELING ZERO-TRUNCATED COUNT DATA
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Abstract
In this paper, a more generalized zero-truncated distribution that come from the mixture of distributions was developed and implemented for non-zero count data. The application of the distribution was demonstrated and its performance assessed against some existing ones using real life datasets. Following the idea of mixed distributions, the Zero-Truncated Com-Binomial (ZTCB) is from the mixture of Conway-Maxwell-Poisson type generalization to the Binomial distribution. The first two moments via probability generating function were also derived. The Maximum Likelihood Estimations of the parameters were also obtained by direct maximization of the log-likelihood function using “optim†routine in R software. The findings of the study showed that: the ZTCB distribution is more robust to handle all levels of dispersion than Zero-Truncated Multiplicative Binomial distribution. The statistics (chi square goodness-of-fit) as well as Deviance (in example four) and the AIC show that the proposed ZTCB distribution yields best result among the models under consideration. This paper therefore provides useful alternative to the existing zero-truncated distributions.
Keywords - Zero-Truncated, Com-binomial, Maximum likelihood, Multiplicative Binomial, structurally non-zero.
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Conway, R. W. and Maxwell, W. L. (1962). A queuing model with state dependent service rates. Journal of Industrial Engineering,
:132-6.
Shmueli G., Borle S., and Boatwright P. (2005). A useful distribution for fitting discrete data: Revival of the Conway-Maxwell-
Poisson distribution. Applied Statistics ;54:127-42.
Jowaheer V, Khan NAM (2009). Estimating regression effects in COM Poisson generalized linear model. World Academy of
Science, Engineering, and Technology, ;53:213-23.
Sellers K.F., and Shmueli G. (2010) A flexible regression model for count data. Annals of Applied Statistics, 4:943-61.
Famoye, F. (1993). Restricted generalized Poisson regression model. Comm. Statist. Theory Methods 22 1335–1354. MR1225247
Zuur A.F., Leno E.N., Walker N.J., SavelievA.and Smith G.M. (2009). Zero-truncated and zero-inflated models for count data. In
mixed effects models and extensions in ecology with R-Statistics for Biology and Health, 1-33.
Borges P, Rodrigues J and Balakrishnan N. (2014). A Compoisson type generalization of the Binomial distribution and its
properties and applications. Statistics and Probability Letters 87.
Aderoju, S.A.,(2017). Zero-Truncated Compoisson-BinomialDistribution and its Application. International Journal of Advanced
Research in Science, Engineering and Technology, (IJARSET), Vol.4,Issue 3
Jolayemi, E.T.(1990). Model selection for One-Dimensional Multinomials. Biom.J.32: 827-834.
R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
URL https://www.R-project.org/.
Shanker R, HagosFesshaye, Sujatha Selvaraj and AbreheYemane (2015), On Zero-Truncation of Poisson and Poisson-Lindley
Distributions and Their Applications, Biometrics & Biostatistics International Journal, Vol 2, Issue 6.
Matthews, J.N.S. and Appleton, D.R. (1993). An application of the truncated Poisson distribution to immunogold assay. Biometrics, 49,
–621
Thomas D.G. and Gart J.J. (1971). Small sample performance of some estimators of the truncated binomial distribution. Journal of the
American Statistical Association, 66, 169-175.
Elamir E.A.H, (2013). Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data
Generation. Journal of Statistical Theory and Applications, Vol. 12, No. 1 (May 2013), 92-105