Abstract-We use the Dichotomous Markov Noise (DMN) model with constant transition rates to describe the dynamics of fluctuations in the water level as a stochastic process, which is imposed on river discharge changes. By applying this model, two different regimes are determined for the long-term behaviour of the river. Based on these regimes, we define two nonparametric classes of the overall increasing/decreasing nature of the water level in the longterm behaviour, which are separated by an exponential steady state regime. In this paper, we develop a nonparametric testing procedure to test exponentially (steady state regime) against an alternative overall decreasing level distribution. The proposed test predicts the long-term regime behaviour of the river. The mathematical tools introduced to handle the problem should be of general use and the testing procedure can be considered as a new mathematical tool in the study of water level dynamics. Under conditions of data austerity and as a case of study, we examine the stochastic characteristics of the Zayandeh Rud 1 River (Isfahan, Iran) water level.
In this paper, we investigate the probabilistic characteristics of a unit driven by Dichotomous Markov Noise (DMN), as an external random life increasing and decreasing shocks. Using DMN, we will define two new aging classes of the overall increasing/decreasing (OIL/ODL) nature in the long time behavior, which are separated by an exponential steady state regime. In addition, a moment inequality is derived for the system whose life distribution is in an overall life decreasing (ODL) class. We use this inequality to devise a nonparametric testing procedure for exponentiality against an alternative overall decreasing life distribution.
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