Tail Probability Ratios of Normal and Student’s t Distributions

Tiejun Tong and Heng Peng

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 18, 3797-3811

Abstract: The ratio of normal tail probabilities and the ratio of Student’s 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.

Date: 2014
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DOI: 10.1080/03610926.2012.701700

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