Monotonicity properties of the gamma family of distributions

被引：6
|
作者：
Pinelis, Iosif [1 ]
机构：
[1] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA
来源：
STATISTICS & PROBABILITY LETTERS | 2021年 / 171卷
关键词：
Stochastic monotonicity; Gamma distribution; Incomplete gamma function; Logarithmic mean; DIFFERENCE;
D O I：
10.1016/j.spl.2020.109027
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：
For real a > 0, let X-a denote a random variable with the gamma distribution with parameters a and 1. Then P(X-a - a > c) is increasing in a for each real c >= 0; non-increasing in a for each real c <= -1/3; and non-monotonic in a for each c is an element of (-1/3, 0). This extends and/or refines certain previously established results. (C) 2020 Elsevier B.V. All rights reserved.
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页数：5
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