On the Hyper-Poisson Distribution and its Generalization with Applications
Journal Title: Journal of Advances in Mathematics and Computer Science - Year 2017, Vol 21, Issue 3
Abstract
In this paper, we fit the hyper-Poisson, and the Mittag-Leffer function (MLFD) distributions to data exhibiting over and under dispersion. Three frequency data sets were employed with one exhibiting under-dispersion. We also extend these distributions to GLM situations where we have a set of covariates defined in the form x ' β. In all, we compared the negative-binomial (NB), the generalized Poisson (GP), the Conway-Maxwell Poisson (COMP), the Hyper-Poisson (HP) and the MLFD models to the selected data sets. The generalized linear model (GLM) data employed in this study is the German national health registry data which has 3874 observations with 41.56% being zeros-thus the data is zero-inflated. Our results contrast the results from these various distributions. Further, theoretical means and variances of each model are computed together with their corresponding empirical means and variances. It was obvious that the two do not match for each of our data sets. The reason being that the models all have infinite range of values than the random variable Y can take, but the data has a finite range of values. It is therefore not unusual for the sum of estimated probabilities being less than 1.00 and consequently, the sum of the expected values are usually less that the sample size n. However, if the range of values of Y are extended beyond the given data value,
Authors and Affiliations
Bayo H. Lawal
Keywords
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- EP ID EP322038
- DOI 10.9734/BJMCS/2017/32184
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