Comparative Analyses of the Poisson-Exponential-Gamma to Selected Discrete Distributions with Applications

In this paper, we compare results arising from implementing the new Poisson-Exponential-Gamma distribution (PEG) to other competing two-parameter distributions such as the generalized Poisson Lindley (GPL), the Poisson generalized Lindley (PGL), the Negative binomial (NB) and several others to several frequency data sets exhibiting different characteristics and data with covariates exhibiting over-or-under dispersion. In all, we show that the PEG does not perform better than most existing distributions. We also demonstrate the equivalence of the GPL and the PGL (the latter being a re-parameterized version of the former). We further show that the New Poisson generalized Lindley (NGPL) distribution is also equivalent to the two-parameter discrete Lindley (TDL) distribution and that in some cases, these two degenerate to the one-parameter geometric distribution (GD). Our results here indicate the limitations of the PEG especially to under-dispersed data. For very strong over-dispersed data, the NB, the New logarithmic distribution (NLD), the New Geometric Discrete Pareto Distribution (NGDP) or the discreteWeibull(DW) perform much better. SAS PROC NLMIXED is employed in our estimation. Adjusted group X2 as well as Wald’s test statistics were computed using estimated theoretical means and variances.