Department of Mathematics
The ratio of normal tail probabilities and the ratio of Students t tail probabilities have gained an increased attention in statistics and related areas. However, they are not well studied in the literature. In this paper, we systematically study the functional behaviors of these two ratios. Meanwhile, we explore their difference as well as their relationship. It is surprising that the two ratios behave very different to each other. Finally, we conclude the paper by conducting some lower and upper bounds for the two ratios.
Lower bound, Normal distribution, Student's t distribution, Tail probability ratio, Upper bound
Source Publication Title
Communications in Statistics - Theory and Methods
Taylor & Francis
This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Statistics - Theory and Methods in September 2014, available online: http://www.tandfonline.com/10.1080/03610926.2012.701700.
Link to Publisher's Edition
Tong, T., & Peng, H. (2014). Tail probability ratios of normal and student’s t distributions. Communications in Statistics - Theory and Methods, 43 (18), 3797-3811. https://doi.org/10.1080/03610926.2012.701700