Expectiles, Omega Ratios and Stochastic Ordering
Expectiles, Omega Ratios and Stochastic Ordering
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DOI：
10.1007/s11009-016-9527-2
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发表时间：
2016-11
影响因子：
0.9
通讯作者：
Fabio Bellini;B. Klar;A. Müller
中科院分区：
文献类型：
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作者：
Fabio Bellini;B. Klar;A. Müller
本文引入了期望序，定义为对每个α∈（0，1），X ≤eYifeα（X）≤eα（Y），其中α表示α-期望.我们证明了期望序等价于Omega比的逐点序，并给出了几个充要条件。在平均值相等的情况下，期望序可以很容易地通过停止损失变换来表征;在更一般的不同平均值的情况下，我们提供了一些充分条件。与更常见的随机序（如≤stand ≤cx）相比，期望序不是由一类效用函数生成的，并且关于卷积不是封闭的。作为一个例子，我们比较了Lomax分布族中的≤st，≤ icx和≤eorders，并比较了拟合到美国自然灾害的真实的数据的Lomax分布。
In this paper we introduce theexpectile order, defined byX≤eYifeα(X) ≤eα(Y) for eachα∈ (0, 1), whereeαdenotes theα-expectile. We show that the expectile order is equivalent to the pointwise ordering of the Omega ratios, and we derive several necessary and sufficient conditions. In the case of equal means, the expectile order can be easily characterized by means of the stop-loss transform; in the more general case of different means we provide some sufficient conditions. In contrast with the more common stochastic orders such as ≤stand ≤cx, the expectile order is not generated by a class of utility functions and is not closed with respect to convolutions. As an illustration, we compare the ≤st, ≤icxand ≤eorders in the family of Lomax distributions and compare Lomax distributions fitted to real world data of natural disasters in the U.S. caused by different sources of weather risk like storms or floods.