Tail probability ratios of normal and students t distributions

Tiejun Tong*, Heng Peng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)
31 Downloads (Pure)


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 languageEnglish
Pages (from-to)3797-3811
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Issue number18
Publication statusPublished - 26 Aug 2014

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Lower bound
  • Normal distribution
  • Student's t distribution
  • Tail probability ratio
  • Upper bound


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