On Zero Truncated Under-dispersed Count Data

Abstract

In this paper, we employ two and three parameter distributions to model the under-dispersed zero truncated data presented in a recent article. We illustrate with a large frequency data having many categories that, the zero-truncated negative binomial and its mixture distributions always fail to converge and consequently producing estimated probabilities that sum more than 1 within the range of the data. The two-parameter zero-truncated versions of the following distributions are considered here: the generalized Poisson (ZTGP), the new logarithmic distribution (ZTNLD), the new geometric discrete Pareto distribution (ZTNGDP), the generalized Poisson-Lindley (ZTGPLD), the zero-truncated Poisson-Exponential-Gamma (ZTPEGD) and the Quasi-Negative Binomial (ZTQNBD2). The three-parameter distributions similarly considered include the zero-truncated Quasi-negative binomial (ZTQNBD), the zero-truncated Inverse Trinomial (ZTIT), the zero-truncated Delaporte (ZTDLPD), the zero-truncated Negative binomialErlang distribution (ZTNB-ELD), the New three parameter Poisson-Lindley distribution (ZTNTPLD) and the New three-parameter size-biased Poisson- Lindley distribution (NTPSBPLD) zero-truncated versions. Three frequency data sets were employed and we further extend our analyses to zero-truncated count data having co-variates (GLM) by utilizing the Nigerian Health Insurance Survey (NHIS) data. Among the models, the ZTPEGD and the ZTDLPD perform better than all the other models for the example datasets employed in this study. The Delaporte is particularly attractive and easier to program in R since there is a Delaporte package in R that can be appropriately used. All models in
this study were implemented with SAS NLMIXED and corresponding written R codes. Two of the R codes are presented in Appendices I and II.