• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.493-504
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• 2017

We often observe count data that exhibit over-dispersion, originating from too many zeros, and under-dispersion, originating from too few zeros. To handle this types of problems, the zero-altered distribution model is designed by Ghosh and Kim in 2007. Their model can control both over-dispersion and under-dispersion with a single parameter, which had been impossible ever. The dispersion type depends on the sign of the parameter ${\delta}$ in zero-altered distribution. In this study, we demonstrate the role of the dispersion type parameter ${\delta}$ through the data of the number of births in Korea. Employing both the chi-square statistic and the Kolmogorov statistic for goodness-of-fit, we also explained any difference between the theoretical distribution and the observed one that exhibits either over-dispersion or under-dispersion. Finally this study shows whether the test statistics for goodness-of-fit show any similarity with the role of the dispersion type parameter ${\delta}$ or not.