![]() As proved by Cooley (2013), the EWT and ENE are affected differently by nonstationarity, possibly producing ambiguity in engineering design practice (Du et al., 2015 Read and Vogel, 2015). For example, the return period may be reformulated in two different ways, the “expected waiting time” (EWT Olsen et al., 1998) or the “expected number of events” (ENE Parey et al., 2007, 2010), which lead to a different evaluation of quantiles within a nonstationary approach. Thus, several considerations should be made with respect to updating some important hydrological concepts while assuming that the non-exceedance probability varies with time or other covariates. In this context, detecting the existence of time-dependence in a stochastic process should be considered a necessary task in the statistical analysis of recorded time series. ![]() As Koutsoyiannis and Montanari (2015) depicted in their historical review of the “concept of stationarity”, Kolmogorov, in 1931, “used the term stationary to describe a probability density function that is unchanged in time”, whereas Khintchine (1934) provided a formal definition of stationarity of a stochastic process. They are usually obtained after fitting a probabilistic model to observed data. One of the main goals of extreme event frequency analysis is the estimation of distribution quantiles related to a certain non-exceedance probability. Phenomena, can be considered as stochastic processes (Chow, 1964), i.e., families of random variables with an assigned probability distribution, and time series are the observable part of this process. Streamflow, as well as temporal rainfall and many other hydrological Nonstationary conditions is one of the major challenges of our times. ![]() The long- and medium-term prediction of extreme hydrological events under The power and efficiency of parameter estimation, including the trend coefficient, were investigated via Monte Carlo simulations using the generalized extreme value distribution as the parent with selected parameter sets. The aim of this study is to compare the performance of parametric and nonparametric methods for trend detection, analyzing their power and focusing on the use of traditional model selection tools (e.g., the Akaike information criterion and the likelihood ratio test) within this context. In this light, the focus is shifted toward model selection criteria this implies the use of parametric methods, including all of the issues related to parameter estimation. Although the time series trend or change points are usually detected using nonparametric tests available in the literature (e.g., Mann–Kendall or CUSUM test), the correct selection of the stationary or nonstationary probability distribution is still required for design purposes. Considering that the available hydrological time series can be recognized as the observable part of a stochastic process with a definite probability distribution, two main topics can be tackled in this context: the first is related to the definition of an objective criterion for choosing whether the stationary hypothesis can be adopted, whereas the second regards the effects of nonstationarity on the estimation of distribution parameters and quantiles for an assigned return period and flood risk evaluation. The need to fit time series characterized by the presence of a trend or change points has generated increased interest in the investigation of nonstationary probability distributions in recent years.
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