Department of Mathematics
Tail probability ratios of normal and student’s t distributions
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. © 2014 Taylor & Francis Group, LLC.
Lower bound, Normal distribution, Student's t distribution, Tail probability ratio, Upper bound
Source Publication Title
Communications in Statistics - Theory and Methods
Taylor & Francis
Link to Publisher's Edition
Tong, Tiejun, and Heng Peng. "Tail probability ratios of normal and student’s t distributions." Communications in Statistics - Theory and Methods 43.18 (2014): 3797-3811.