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Tail Probability Ratios of Normal and Student’s t Distributions

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  • Tiejun Tong
  • Heng Peng

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.

Suggested Citation

  • Tiejun Tong & Heng Peng, 2014. "Tail Probability Ratios of Normal and Student’s t Distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(18), pages 3797-3811, September.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:18:p:3797-3811
    DOI: 10.1080/03610926.2012.701700
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