Recurrence times and the expected number of renewal epochs over a finite interval

IF 1.2 4区数学 Q2 STATISTICS & PROBABILITY

Statistics Pub Date : 2023-01-02 DOI:10.1080/02331888.2023.2172172

Sotirios Losidis

引用次数: 0

Abstract

This paper initially presents bounds for the joint tail and the conditional tails of the backward and forward recurrence times. Using these bounds, we deliver an improvement to the lower bound for the renewal function given by Brown [Inequalities for distributions with increasing failure rate. In: Gelfand AE, editors. Contributions to the theory and applications of statistics, a volume in honour of Herbert Solomon. Orlando, FL: Academic; 1987. p. 3–17] for IFR inter-arrival times. Finally, this paper proposes a renewal type equation for the expected number of renewals in and, under certain conditions, improves Lorden's [On excess over the boundary. Ann Math Stat. 1970;41(2):520–527] well-known general upper bound for the expected number of renewals in .

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在有限区间内的递归次数和更新历元的期望次数

本文首先给出了前后递归时间的联合尾和条件尾的界。利用这些边界，我们改进了Brown[不等式]给出的关于故障率增加的分布的更新函数的下界。编辑:Gelfand AE。对统计理论和应用的贡献，一卷纪念赫伯特·所罗门。佛罗里达州奥兰多:学术;1987. (p. 3-17)查询IFR到达时间。最后，在一定条件下，提出了期望更新次数的更新型方程，改进了边界上的洛登[On]过剩。[j] .数学统计，2007;41(2):520-527]。

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 数学-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.