On the Normal Approximation for Some Special Estimators of the Ratio of Binomial Proportions

Parichart  Pattarapanitchai; Kamon  Budsaba; Tran  Loc Hung; Andrei  Volodin

On the Normal Approximation for Some Special Estimators of the Ratio of Binomial Proportions

Authors

Parichart Pattarapanitchai Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Rangsit Campus, Pathum Thani, Thailand
Kamon Budsaba Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Rangsit Campus, Pathum Thani, Thailand
Tran Loc Hung Faculty of Basic Sciences, University of Finance and Marketing, Ho Chi Minh, Vietnam
Andrei Volodin Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada

Keywords:

Point estimators, ratio of binomial proportions, inverse binomial sampling, direct binomial sampling, normal asymptotic of an estimator

Abstract

We focus on the normal approximation for special cases of point estimators of the ratio of Binomial proportions of two independent populations. We prove that these estimators are normally distributed, something that has not been done before. We investigate its performance in terms of bias, variance, and mean square error, using Monte Carlo simulations. The results show that the normal approximation, which is relatively simple, provides a reliable result. The normal approximation approach could be recommended on the basis of the specific values of the parameters and/or sample sizes.

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Published

2022-09-29

How to Cite

Pattarapanitchai, P. ., Budsaba, K. ., Loc Hung, T. ., & Volodin, A. . (2022). On the Normal Approximation for Some Special Estimators of the Ratio of Binomial Proportions. Thailand Statistician, 20(4), 779–790. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/247460