Robust Confidence Interval Estimation Method for the Mean of Poisson Distribution to Handle Outliers

Juthaphorn Sinsomboonthong; Saichon Sinsomboonthong

doi:10.6180/jase.202208_25(4).0020

Robust Confidence Interval Estimation Method for the Mean of Poisson Distribution to Handle Outliers

Physics

Juthaphorn Sinsomboonthong This email address is being protected from spambots. You need JavaScript enabled to view it.¹ and Saichon Sinsomboonthong²

¹Department of Statistics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand
²Department of Statistics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Received: July 31, 2021
Accepted: October 18, 2021
Publication Date: December 6, 2021

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202208_25(4).0020

ABSTRACT

In this article, the robust confidence interval estimation method for the Poisson mean to handle outliers in data set is presented. The proposed technique is called median bootstrap confidence interval or BC−Med method. The simulation study was constructed 160 situations to compare the efficiency for two criteria—the coverage probability and the average width—of five methods, namely, Wald, WaldC, Bégaud, Brown and BC−Med methods. It is found that in case of non-outliers in the data set, Brown method tends to have the desirable performance for almost all levels of the Poisson means and all sample sizes n. Furthermore, the efficiency of Wald method is also as good as that of Brown method for the sample sizes are not less than 30 and almost all levels of the Poisson means when data set is not contaminated with outliers. In case of outliers in the data set, BC−Med method tends to have the most efficiency for all levels of sample sizes n and almost all levels of the Poisson means. The findings will be useful for researchers to more accurately estimate the mean of Poisson distribution when sample data are contaminated with outliers, e.g., estimation of the number of deaths from accidents per day. Because the BC−Med method was developed from a robust location estimator, therefore outliers have slightly influence on the Poisson mean estimation for this proposed method.

Keywords: average width; bootstrap confidence interval; coverage probability; Poisson mean

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