Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 3797-3811 |
| Number of pages | 15 |
| Journal | Communications in Statistics - Theory and Methods |
| Volume | 43 |
| Issue number | 18 |
| DOIs | |
| Publication status | Published - 26 Aug 2014 |
User-Defined Keywords
- Lower bound
- Normal distribution
- Student's t distribution
- Tail probability ratio
- Upper bound