The Stieltjes transform order and related ratio order

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2026-06-01 Epub Date: 2026-02-02 DOI:10.1016/j.spl.2026.110663

Abdulaziz Alenazi , Khaled Mehrez

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引用次数: 0

Abstract

In this paper, we introduce the Stieltjes transform order, defined via the composition of the Laplace transform of a random variable. First, we establish the monotonicity of the hazard rate associated with a transformed distribution of a random variable

X

. As a consequence, we derive a sharp lower bound for the Stieltjes transform of

X

in terms of its first two inverse moments. Secondly, we investigate the Stieltjes transform ratio order and provide its characterizations, both via properties of the hazard rate and through the monotonicity properties of higher-order Stieltjes transforms together with moment inequalities. We further establish explicit connections between the proposed orders and classical stochastic orders, including equivalence with the usual stochastic order and implication from the likelihood ratio order. These results enhance our understanding of stochastic orders and open new avenues for applications in reliability theory, economics, and applied probability.

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Stieltjes变换阶和相关的比值阶

本文引入了Stieltjes变换阶，它是由随机变量的拉普拉斯变换的复合定义的。首先，我们建立了与随机变量X的变换分布相关的风险率的单调性。因此，我们根据X的前两个逆矩导出了X的Stieltjes变换的明显下界。其次，通过危险率的性质和高阶Stieltjes变换与矩不等式的单调性性质，研究了Stieltjes变换比阶，并给出了其表征。我们进一步建立了所提阶与经典随机阶之间的明确联系，包括与通常随机阶的等价性和来自似然比阶的暗示。这些结果增强了我们对随机顺序的理解，并为可靠性理论、经济学和应用概率的应用开辟了新的途径。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

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