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

被引：0

作者：

Chadjiconstantinidis, Stathis ^{[1
]}

Politis, Konstadinos ^{[1
,2
]}

机构：

[1] Univ Piraeus, Dept Stat & Insurance Sci, Piraeus, Greece

[2] Univ Piraeus, Dept Stat & Insurance Sci, 80 Karaoli & Dimitriou str, Piraeus, Greece

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 454卷

关键词：

Renewal process; Renewal equation; Joint distribution; Recurrence times; Bounds; MONOTONICITY PROPERTIES; INEQUALITIES;

D O I：

10.1016/j.cam.2024.116166

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：22

共 31 条

[1] Asmussen S., 2003, APPL PROBABILITY QUE
[2] Barlow R.E., 1996, Statistical Theory of Life Testing: Probability Models
[3] Barza S, 2006, PUBL MATH-DEBRECEN, V68, P139
[4] BOUNDS, INEQUALITIES, AND MONOTONICITY PROPERTIES FOR SOME SPECIALIZED RENEWAL PROCESSES
BROWN, M
[J]. ANNALS OF PROBABILITY, 1980, 8 (02) : 227 - 240
[5] Brown M., 1987, Contributions to the Theory and Applications of Statistics, A Volume in Honor of Herbert Solomon, P3, DOI DOI 10.1016/B978-0-12-279450-6.50010-5
[6] Aging properties and bounds for ruin probabilities and stop-loss premiums
Cai, J
Garrido, J
[J]. INSURANCE MATHEMATICS & ECONOMICS, 1998, 23 (01) : 33 - 43
[7] Sequences of Improved Two-Sided Bounds for the Renewal Function and the Solutions of Renewal-Type Equations
Chadjiconstantinidis, Stathis
[J]. METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2023, 25 (02)
[8] Some bounds for the renewal function and the variance of the renewal process
Chadjiconstantinidis, Stathis
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2023, 436
[9] Improved bounds for the solutions of renewal equations
Chadjiconstantinidis, Stathis
Tzavelas, George
[J]. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 2023, 37 (03) : 740 - 777
[10] Feller W., 2008, An introduction to probability theory and its application, V2

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