Probability Distribution of Waiting Time of the th Extreme Event under Serial Dependence
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Volume 25, Issue 6
Abstract
Negative binomial distribution has been suggested to describe the first arrival time of the th flood exceeding the design flood under independence and both stationary and nonstationary conditions. However, hydrological processes often exhibit temporal dependence, which can cause persistent fluctuations in observed series and clustering of extreme events that might be confused with nonstationary effects. This study focuses on a distribution of waiting time of the th event exceeding a prescribed design value under stationarity and serial dependence. This probability distribution is known as beta negative binomial, which complements the models proposed for (non)stationary independent processes, and enables the comparison with results corresponding to stationary dependent processes. We discuss the properties of the beta negative binomial distribution and show its validity for theoretical occurrence processes with power-law and exponentially decaying autocorrelation functions. The proposed model is applied to peak flows and maximum temperatures recorded across the conterminous United States. Results show that the beta negative binomial distribution can capture the effect of serial dependence on the distribution of waiting time of extreme events.
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Data Availability Statement
Peak flow data used in this study are freely available in the supplemental material of Hirsch and Ryberg (2012) at https://doi.org/10.1080/02626667.2011.621895 and from the USGS via the National Water Information System (NWIS) online database (USGS 2016). Temperature data are provided by the National Oceanic and Atmospheric Administration (NOAA) through the US Climate Divisional Database (Vose et al. 2014b). The analyses were performed in R (R Core Team 2019).
Acknowledgments
Francesco Serinaldi acknowledges the support from the Willis Research Network and dedicates this study to Giacomo Serinaldi (1932–2018). Federico Lombardo is grateful to the Italian National Fire and Rescue Service for the continuous support. The authors thank two anonymous reviewers for their constructive remarks.
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Journal of Hydrologic Engineering
Volume 25 • Issue 6 • June 2020
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©2020 American Society of Civil Engineers.
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Received: Aug 12, 2019
Accepted: Dec 17, 2019
Published online: Apr 8, 2020
Published in print: Jun 1, 2020
Discussion open until: Sep 8, 2020
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