A quantile inequality for location-scale distributions

被引：1
|
作者：
Elster, Clemens [1 ]
Klauenberg, Katy [1 ]
机构：
[1] Phys Tech Bundesanstalt, Abbestr 2-12, D-10587 Berlin, Germany
来源：
STATISTICS & PROBABILITY LETTERS | 2020年 / 165卷
关键词：
Quantile inequality; Location-scale distribution; Attribute sampling; AREA;
D O I：
10.1016/j.spl.2020.108851
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：
It is shown that when X follows a location-scale distribution with continuous density function that has support R and 0 < q < p < 1, then P(vertical bar X vertical bar <= Delta) >= q implies P(vertical bar X vertical bar <= lambda Delta) >= p for some lambda > 1 and all values of the location and scale parameters. An explicit expression for the minimum lambda is proven for the family of scaled and shifted t-distributions. (C) 2020 Elsevier B.V. All rights reserved.
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页数：6
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