Bounds for the distribution and moments of the forward and backward recurrence times in a renewal process

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-07-24 DOI:10.1016/j.cam.2024.116166

Stathis Chadjiconstantinidis, Konstadinos Politis

引用次数: 0

Abstract

We obtain a variety of lower and upper bounds for the bivariate tail of the joint distribution between the (forward and backward) recurrence times in a renewal process. Some of these bounds are valid generally, some others in the case where the interarrival distribution $F$ exhibits monotone aging. We also give various bounds for the moments of the recurrence times. Our results improve upon existing bounds for these quantities in the literature. We also discuss the case where the aging of $F$ is non-monotonic. Finally, we present numerical examples to illustrate the performance of the new bounds.

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更新过程中前向和后向递推时间的分布和矩的边界

我们得到了更新过程中（前向和后向）递归时间联合分布的双变量尾部的各种下限和上限。其中一些边界在一般情况下有效，另一些则在到达间分布 F 呈现单调老化的情况下有效。我们还给出了递推时间矩的各种约束。我们的结果改进了文献中对这些量的现有约束。我们还讨论了 F 的老化是非单调的情况。最后，我们通过数字示例来说明新边界的性能。

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.