On the Krawtchouk expansion for estimating counting data

Abstract

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 flexible to model under-, equi- and over dispersed data. The classical Weldon's data was revisited to show the flexibility and accuracy of the proposed expansion.