References
- Feller W. An introduction to probability theory and its applications. 2nd ed. Vol. II, New York: Wiley; 1971.
- Willmot GE, Lin X. Lundberg approximations for compound distributions with insurance applications. New York: Springer; 2001.
- Brown M. Bounds, inequalities, and monotonicity properties for some specialised renewal processes. Ann Probab. 1980;8:227–240. doi: 10.1214/aop/1176994773
- Brown M. Further monotonicity properties for specialized renewal processes. Ann Probab. 1981;9:891–895. doi: 10.1214/aop/1176994317
- Shaked M, Zhu H. Some results on block replacement policies and renewal theory. J Appl Probab. 1992;29:932–946. doi: 10.2307/3214725
- Gakis KG, Sivazlian BD. The correlation of the backward and forward recurrence times in a renewal process. Stoch Anal Appl. 1994;12(5):543–549. doi: 10.1080/07362999408809372
- Losidis S, Politis K. Moments of the forward recurrence time in a renewal process. Methodol Comput Appl Probab. 2020;22(4):1591–1600. doi: 10.1007/s11009-018-9681-9
- Chen YH. Classes of life distributions and renewal counting process. J Appl Probab. 1994;31(4):1110–1115. doi: 10.2307/3215334
- Losidis S, Politis K, Psarrakos G. Exact results and bounds for the joint tail and moments of the recurrence times in a renewal process. Methodol Comput Appl Probab. 2021;23(4):1489–1505. doi: 10.1007/s11009-020-09787-w
- Barlow RE, Proschan F. Statistical theory of reliability and life testing. MD: Silver Spring; 1981. Reprint Edition. To begin with.
- Losidis S. Recurrence times and the expected number of renewal epochs over a finite interval. Statistics. 2023;57(1):195–212. doi: 10.1080/02331888.2023.2172172
- Losidis S, Politis K. Bounds for the renewal function and related quantities. Methodol Comput Appl Probab. 2022;24:2647–2660. doi: 10.1007/s11009-022-09953-2
- Barlow RE, Proschan F. Mathematical theory of reliability. SIAM; 1996. (Classics in applied mathematics).
- Gut A. Stopped random walks: limit theorems and applications. New York: Springer-Verlag; 2009.
- Coleman R. The moments of the forward recurrence time. Eur J Oper Res. 1982;9(2):181–183. doi: 10.1016/0377-2217(82)90070-4
- Chadjiconstantinidis S. Some bounds for the renewal function and the variance of the renewal process. Appl Math Comput. 2023;436:127497.
- Aydogdu H, Ozturk F. Some bounds for the variance function in renewal processes. Commun Fac Sci Univ Ank Ser A1 Math Stat. 1998;47:85–96.
- Willmot GE, Cai J, Lin XS. Lundberg inequalities for renewal equations. Adv Appl Probab. 2001;33:674–689. doi: 10.1239/aap/1005091359
- Woo J–K. Refinements of two-sided bounds for renewal equations. Ins Math Econ. 2011;48:189–196. doi: 10.1016/j.insmatheco.2010.10.013
- Chadjiconstantinidis S, Politis K. Non-exponential bounds for stop-loss premiums and ruin probabilities. Scand Act J. 2005;2005(5):335–357. doi: 10.1080/03461230510009817
- Chadjiconstantinidis S, Politis K. Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model. Ins Math Econ. 2007;41(1):41–52. doi: 10.1016/j.insmatheco.2006.09.001
- Politis K, Koutras MV. Some new bounds for the renewal function. Prob Eng Inf Sci. 2006;20:231–250. doi: 10.1017/S0269964806060141
- Jiang R. A simple approximation for the renewal function with an increasing failure rate. Reliab Eng Syst Saf. 2010;95(9):963–969. doi: 10.1016/j.ress.2010.04.007
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