Application of the Cramer-von Mises type optimization to a binomial distribution

Abstract

This paper proposes the novel estimator for the success probability parameter of a binomial distribution. To that end, we use the Cramer-von Mises type optimization methodology which has been popular for the parameter estimation in continuous distributions. Upon obtaining the estimator, desirable properties of the proposed estimation method such as asymptotic distribution and robustness are rigorously investigated. Simulation studies demonstrate that the proposed estimator compares favorably with other well-celebrated estimators