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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