Abstract
In this paper, we investigate the probabilistic characteristics of systems driven by dichotomous Markov noise (DMN), described by an external random increasing and decreasing shocks. Based on the DMN, we define two new aging classes of the increasing/decreasing renewal dichotomous Markov noise (IRDMN/DRDMN), which are separated by an exponential steady state regime in the long time behavior. In addition, a moment inequality is derived for the system whose life belongs to DRDMN class. This inequality to devise a nonparametric testing procedure for exponentiality against an alternative DRDMN life distributions.
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Sepehrifar, M., Yarahmadian, S. Decreasing renewal dichotomous Markov noise shock model with hypothesis testing applications. Stat Papers 58, 1115–1124 (2017). https://doi.org/10.1007/s00362-016-0740-4
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DOI: https://doi.org/10.1007/s00362-016-0740-4