Asymptotic tail properties of student's t-distribution

被引：16

作者：

Finner, Helmut ^{[1
]}

Dickhaus, Thorsten ^{[1
]}

Roters, Markus ^{[2
]}

机构：

[1] Univ Dusseldorf, Leibniz Ctr, German Diabet Ctr, Inst Biometr & Epidemiol, D-40225 Dusseldorf, Germany

[2] Omnicare Clin Res, Biometr Dept, Cologne, Germany

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2008年 / 37卷 / 02期

关键词：

large deviations; likelihood ratio; Mills' ratio; t-distribution; zone of normal convergence;

D O I：

10.1080/03610920701649019

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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

引用

页码：175 / 179

页数：5

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