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Dependence Modeling

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A generalized class of correlated run shock models

Femin Yalcin / Serkan Eryilmaz / Ali Riza Bozbulut
Published Online: 2018-06-28 | DOI: https://doi.org/10.1515/demo-2018-0008

Abstract

In this paper, a generalized class of run shock models associated with a bivariate sequence {(Xi, Yi)}i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X1, X2, ... over time, let the random variables Y1, Y2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑Nt=1 Yt , where N is a stopping time for the sequence {Xi}i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {Xi, 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.

Keywords : Compound distributions; Dependence; Laplace transform; Phase-type distributions; Shock models

References

  • [1] Anderson, K. K. (1988). A note on cumulative shock models. J. Appl. Probab. 25(1), 220-223.Google Scholar

  • [2] Cirillo, P. and J. Hüsler (2011). Extreme shock models: An alternative perspective. Stat. Probab. Lett. 81(1), 25-30.Web of ScienceGoogle Scholar

  • [3] Eryilmaz, S. (2012). Generalized δ-shock model via runs. Stat. Probab. Lett. 82(2), 326-331.Web of ScienceGoogle Scholar

  • [4] Eryilmaz, S. (2013). On the lifetime behavior of a discrete time shock model. J. Comput. Appl. Math. 237(1), 384-388.Web of ScienceGoogle Scholar

  • [5] Eryilmaz, S. (2017a). Computing optimal replacement time and mean residual life in reliability shock models. Comput. Ind. Eng. 103, 40-45.Google Scholar

  • [6] Eryilmaz, S. (2017b). On compound sums under dependence. Insurance Math. Econom. 72, 228-234.Google Scholar

  • [7] Gut, A. (1990). Cumulative shock models. Adv. in Appl. Probab. 22(2), 504-507.Google Scholar

  • [8] Gut, A. (2001). Mixed shock models. Bernoulli. 7(3), 541-555.Google Scholar

  • [9] Gut, A. and J. Hüsler (1999). Extreme shock models. Extremes 2(3), 293-305.Google Scholar

  • [10] Li, Z., Chan L. Y. and Z. Yuan (1999). Failure time distribution under a _-shock model and its application to economic design of system. Int. J. Rel. Qual. Saf. Eng. 6(3), 237-247.Google Scholar

  • [11] Li, Z. and X. Kong (2007). Life behavior of _-shock model. Stat. Probab. Lett. 77(6), 577-587.Google Scholar

  • [12] Mallor, F. and E. Omey (2001). Shocks, runs and random sums. J. Appl. Probab. 38(2), 438-448.CrossrefGoogle Scholar

  • [13] Neuts, M. F. (1981).Matrix-Geometric Solutions in StochasticModels: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore MD.Google Scholar

  • [14] Nikoloulopoulos, A. K. and D. Karlis (2008). Fitting copulas to bivariate earthquake data: The seismic gap hypothesis revisited. Environmetrics 19(3), 251-269.CrossrefWeb of ScienceGoogle Scholar

  • [15] Ozkut, M. and I. Bayramloglu (Bairamov) (2014). On Marshall-Olkin type distribution with effect of shock magnitude. J. Comput. Appl. Math. 271, 150-162.Web of ScienceGoogle Scholar

  • [16] Parvardeh, A. and N. Balakrishnan (2015). On mixed _-shock models. Stat. Probab. Lett. 102, 51-60.Google Scholar

  • [17] Sumita, U. and J. G. Shanthikumar (1985). A class of correlated cumulative shock models. Adv. in Appl. Probab. 17(2), 347-366.Google Scholar

  • [18] Tank, F. and S. Eryilmaz (2015). The distributions of sum, minima and maxima of generalized geometric random variables. Statist. Papers. 56(4), 1191-1203Google Scholar

About the article

Received: 2018-03-09

Accepted: 2018-05-22

Published Online: 2018-06-28


Citation Information: Dependence Modeling, Volume 6, Issue 1, Pages 131–138, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2018-0008.

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© 2018 Femin Yalcin, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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