Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes
In this paper we study stochastic comparisons and dependence properties for the epoch and inter epoch times of trend renewal processes which share a baseline renewal process and with different trend functions. These results extend some of the results on the nonhomogeneous Poisson process in Belzunce et al. [1,2] to those on trend renewal process. Some applications of the obtained results to a shock model, a repair process and some specific class of intermediate order statistics are provided.
[1] Belzunce, F., Lillo, R.E., Ruiz, J.M. & Shaked, M. (2001). Stochastic comparisons of nonhomogeneous processes Probability in the Engineering and Informational Sciences 15: 199-224.
[2] Belzunce, F., Mercader, J.A. & Ruiz, J.M. (2003). Multivariate aging notions of epoch times of nonhomogeneous processes {\it Journal of Multivariate Analysis 84: 335-350.
Palabras clave / Keywords: trend renewal epoch times stochastic ordering multivariate dependence
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