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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Tail probability ratios of normal and student’s t distributions

Language

English

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. © 2014 Taylor & Francis Group, LLC.

Keywords

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

Publication Date

2014

Source Publication Title

Communications in Statistics - Theory and Methods

Volume

43

Issue

18

Start Page

3797

End Page

3811

Publisher

Taylor & Francis

ISSN (print)

03610926

ISSN (electronic)

1532415X

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