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Similarity between the dispersion parameter in zero-altered model and the two goodness-of-fit statistics
Journal of the Korean Data & Information Science Society 2017;28:493-504
Published online May 31, 2017
© 2017 Korean Data & Information Science Society.

Yujeong Yun1 · Honggie Kim2

1Research Division, Asia Pacific Population Institute
2Department of Information and Statistics, Chungnam National University
Correspondence to: Honggie Kim
Professor, Department of Information and Statistics, CNU, 99, Daehak-ro, Yuseong-gu, Daejeon, Republic of Korea. E-mail:
Received April 8, 2017; Revised May 15, 2017; Accepted May 18, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 δ in zero-altered distribution. In this study, we demonstrate the role of the dispersion type parameter δ 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 δ or not.
Keywords : Kolmogorov test, over-dispersion, under-dispersion, zero-altered model, zero deflation, zero inflation.