search for


On the Krawtchouk expansion for estimating counting data
Journal of the Korean Data & Information Science Society 2019;30:693-702
Published online May 31, 2019;
© 2019 Korean Data and Information Science Society.

Hyung-Tae Ha1

1Department of Applied Statistics, Gachon University
Correspondence to: Associate professor, Department of Applied Statistics, Gachon University, Sungnam-ci, Kyunggi-do 461-701. Korea. E-mail:
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2017R1E1A1A03070290).
Received April 30, 2019; Revised May 16, 2019; Accepted May 16, 2019.
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 propose Krawtchouk expansion estimates for modeling count data. The proposed estimate is based on series expansions of discrete Krawtchouk orthogonal polynomials around a binomial distribution. The parameters of the proposed expansion can be estimated via the method of moments or the maximum likelihood method. The proposed expansion is exible to model under-, equi- and over dispersed data. The classical Weldon's data was revisited to show the exibility and accuracy of the proposed expansion.
Keywords : binomial distribution, counting data, dispersion, Krawtchouk polynomials, Weldon's data