About the Authors

Ie-Bin Lian

Affiliation Graduate Institute of Statistics and Information Science, National Changhua University of Education, Changhua, Taiwan

Hong-Dar Isaac Wu

Affiliations Department of Applied Math, National Chung-Hsing university, Taichung, Taiwan, Institute of Statistics, National Chung-Hsing university, Taichung, Taiwan

Wan-Tzu Chang

Affiliation Graduate Institute of Statistics and Information Science, National Changhua University of Education, Changhua, Taiwan

Day-Yu Chao

dychao@nchu.edu.tw

Affiliation Graduate Institute of Microbiology and Public Health, College of Veterinary Medicine, National Chung-Hsing university, Taichung, Taiwan

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: IBL HDW DYC. Performed the experiments: WTC. Analyzed the data: WTC HDW. Contributed reagents/materials/analysis tools: IBL DYC. Wrote the paper: IBL DYC.