Document Type

Journal Article

Department/Unit

Department of Mathematics

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.

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

Peer Reviewed

1

Copyright

This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Statistics - Theory and Methods in September 2014, available online: http://www.tandfonline.com/10.1080/03610926.2012.701700.

DOI

10.1080/03610926.2012.701700

ISSN (print)

03610926

ISSN (electronic)

1532415X

Included in

Mathematics Commons

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