A PURE-TAIL ORDERING BASED ON THE RATIO OF THE QUANTILE FUNCTIONS
成果类型：
Article
署名作者：
ROJO, J
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348541
发表日期：
1992
页码：
570-579
关键词：
摘要：
In the intuitive approach, a distribution function F is said to be not more heavily tailed than G if lim sup(x --> infinity) FBAR/GBAR < infinity. An alternative is to consider the behavior of the ratio F-1(u)/G-1(u), in a neighborhood of one. The present paper examines the relationship between these two criteria and concludes that the intuitive approach gives a more thorough comparison of distribution functions than the ratio of the quantile functions approach in the case F or G have tails that decrease faster than, or at, an exponential rate. If F or G have slowly varying tails, the intuitive approach gives a less thorough comparison of distributions. When F or G have polynomial tails, the approaches agree.