On the negative binomial-generalized exponential distribution and its applications

Abstract

In this paper, we fit the negative binomial-generalized exponential (NB-GE) distribution to data exhibiting excess zeros. Thus we employed the NB-GE and its zero-inflated derivative to three sets of frequency data that have been employed in standard literature on the subject. Our results are compared with both the Poisson, negative binomial and corresponding zero-inflated distributions (ZIP and ZINB). All analyses were carried out using PROC NLMIXED in SAS. Parameter estimates, as well as the expected frequencies under each model and the corresponding goodness-of-fit statistics are computed. Our results extend previous results on the analyzes of the chosen data in this example. Further, results obtained here indicate that some results in earlier studies on some of the example data sets employed in this study may be inaccurate. In others however, our results are consistent with previous analyses on the data sets chosen for this article. While we do not pretend that the results obtained are entirely new, however, the analyses give opportunities to researchers in the field the much needed means of implementing these models in SAS without having to resort to R or Stata. We must also recognize that because the probability mass function of the NB-GE has an infinite value range, estimated probabilities may therefore not necessarily add up to 1.00 over the finite range of values of our discrete random variable and consequently, the sum of estimated expected values may not add up to the observed sample size n.

On Poisson-Samade Distribution: Its Applications in Modelling Count Data

“…In such a scenario, which reflects the presence of overdispersion in the data. "The Poisson model fits overdispersed count data poorly" [1]. Therefore, alternative distributions such as Negative Binomial distribution (NBD), which have a dispersion parameter that accounts for the overdispersion have been proposed [1][2][3][4][5].…”

“…"The Poisson model fits overdispersed count data poorly" [1]. Therefore, alternative distributions such as Negative Binomial distribution (NBD), which have a dispersion parameter that accounts for the overdispersion have been proposed [1][2][3][4][5]. The NBD has pmf defined as: The NBD is suitable for overdispersed count data but may not be appropriate for modelling data exhibiting heavy-tailed.…”