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Asymptotic Tail Properties of Student's t-Distribution

Asymptotic Tail Properties of Student's t-Distribution We investigate the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of Student's t-distribution with ν > 0 degrees of freedom (t ν for short) for ν tending to infinity when the argument x = x ν of the pdf (cdf) depends on ν and tends to ± ∞ (−∞). To this end, we consider the ratio of the pdf's (cdf's) of the t ν- and the standard normal distribution. Depending on the choice of the argument x ν, the pdf-ratio (cdf-ratio) tends to 1, a fixed value greater than 1, or to ∞. As a byproduct, we obtain a result for Mill' ratio when x ν → −∞. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Statistics: Theory and Methods Taylor & Francis

Asymptotic Tail Properties of Student's t-Distribution

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References (13)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1532-415X
eISSN
0361-0926
DOI
10.1080/03610920701649019
Publisher site
See Article on Publisher Site

Abstract

We investigate the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of Student's t-distribution with ν > 0 degrees of freedom (t ν for short) for ν tending to infinity when the argument x = x ν of the pdf (cdf) depends on ν and tends to ± ∞ (−∞). To this end, we consider the ratio of the pdf's (cdf's) of the t ν- and the standard normal distribution. Depending on the choice of the argument x ν, the pdf-ratio (cdf-ratio) tends to 1, a fixed value greater than 1, or to ∞. As a byproduct, we obtain a result for Mill' ratio when x ν → −∞.

Journal

Communications in Statistics: Theory and MethodsTaylor & Francis

Published: Jan 7, 2008

Keywords: Large deviations; Likelihood ratio; Mill' ratio; t -distribution; Zone of normal convergence; Primary 62E20, 60E05; Secondary 60E15, 60F99

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