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In his article Willems (Clim Chang 120(4):931-944, ) proposed a methodology to analyse extremes in rainfall series. When applying it to artificially generated, non-cyclic random variables we were able to detect cyclic behavior. Therefor we had a closer look on the methodology. Here we discuss our considerations, why this method generates cycles, depending on chosen subperiods and their coherence between detected cycle lengths. To verify these relationships some examples based on random data samples are given. [ABSTRACT FROM AUTHOR]

This paper proposes a method from Scan statistics for identifying flood‐rich and flood‐poor periods (i.e., anomalies) in flood discharge records. Exceedances of quantiles with 2‐, 5‐, and 10‐year return periods are used to identify periods with unusually many (or few) threshold exceedances with respect to the reference condition of independent and identically distributed random variables. For the case of flood‐rich periods, multiple window lengths are used in the identification process. The method is applied to 2,201 annual flood peak series in Europe between 1960 and 2010. Results indicate evidence for the existence of flood‐rich and flood‐poor periods, as about 2 to 3 times more anomalies are detected than what would be expected by chance. The frequency of the anomalies tends to decrease with an increasing threshold return period which is consistent with previous studies, but this may be partly related to the method and the record length of about 50 years. In the northwest of Europe, the frequency of stations with flood‐rich periods tends to increase over time and the frequency of stations with flood‐poor periods tends to decrease. In the east and south of Europe, the opposite is the case. There appears to exist a turning point around 1970 when the frequencies of anomalies start to change most clearly. This turning point occurs at the same time as a turning point of the North Atlantic Oscillation index. The method is also suitable for peak‐over‐threshold series and can be generalized to higher dimensions, such as space and space‐time. Plain Language Summary: Flood studies usually assume that the statistical characteristics of flood discharges do not change over time. Here we propose a method for identifying changes in these characteristics. Specifically, we identify periods that exhibit unusually more floods above a threshold and periods with unusually more floods below a threshold. The method goes beyond trend analysis by providing more temporal detail on flood changes. We apply the method to 2,201 observed flood series in Europe between 1960 and 2010. We find that flood‐rich and flood‐poor periods occur in the data, as the number of periods is about 2 to 3 times larger than would be expected by chance. In the northwest of Europe, the number of flood‐rich periods tends to increase over time, while in the east and south of Europe, the opposite is the case. There appears to exist a turning point around 1970 when the frequency of unusual periods starts to change most clearly. This turning point occurs at the same time as a turning point of the North Atlantic Oscillation index suggesting a role in climate fluctuations in the frequency of flood‐rich periods. Key Points: A method from Scan statistics is proposed for identifying flood‐rich and flood‐poor periods in flood discharge recordsThere is evidence of flood‐rich and flood‐poor periods based on analyzing 2,201 flood series in Europe between 1960 and 2010In the northwest of Europe, the frequency of flood‐rich periods tends to increase over time, particularly for large return periods [ABSTRACT FROM AUTHOR]

In 1959, Rényi proposed the information dimension and the $d$ -dimensional entropy to measure the information content of general random variables. This paper proposes a generalization of information dimension to stochastic processes by defining the information dimension rate as the entropy rate of the uniformly quantized stochastic process divided by minus the logarithm of the quantizer step size $1/m$ in the limit as $m\to \infty $. It is demonstrated that the information dimension rate coincides with the rate-distortion dimension, defined as twice the rate-distortion function $R(D)$ of the stochastic process divided by $-\log (D)$ in the limit as $D\downarrow 0$. It is further shown that among all multivariate stationary processes with a given (matrix-valued) spectral distribution function (SDF), the Gaussian process has the largest information dimension rate and the information dimension rate of multivariate stationary Gaussian processes is given by the average rank of the derivative of the SDF. The presented results reveal that the fundamental limits of almost zero-distortion recovery via compressible signal pursuit and almost lossless analog compression are different in general. [ABSTRACT FROM AUTHOR]

This paper presents a geospatial methodology for zoning the earthquake-induced soil liquefaction risk at a continental scale and set-up in a Geographic Information System (GIS) environment by coupling data-driven and knowledge-driven approaches. It is worth mentioning that liquefaction is a phenomenon of soil instability occurring at a very local spatial scale; thus, the mega-zonation of liquefaction risk at a continental scale is a hard facing challenge. Since the risk from natural disasters is the convolution of hazard, vulnerability, and exposure, the liquefaction risk mapping is based on the combination of geospatial explanatory variables, available at the continental scale, of the previously listed three assumed independent random variables. First, by applying a prediction model calibrated for Europe, the probability of liquefaction is mapped for the whole continent. Then, the Analytical Hierarchy Process (AHP) is adopted to identify areas that have a high risk of liquefaction, taking into account proxy data for exposure. The maps are computed for different levels of severity of ground shaking specified by three return periods (i.e., 475, 975, and 2475 years). A broad variety of stakeholders would benefit from the outcomes of this study, such as civil protection organizations, insurance and re-insurance companies, and infrastructure operators. [ABSTRACT FROM AUTHOR]

By using a recursive method, we determine the project completion time when the activity times are distributed according to a beta distribution. The k th moment of the maximum of non-identical independent random variables following this distribution-type is evaluated. Applicability and appropriateness of the beta model are illustrated by some examples, which show that the suggested estimate program evaluted and review technique of the project completion time is located between the lower bound estimate (PERT) and the upper estimate that was obtained by Kambarowski An upper bound on the expected completion time of PERT networks, Eur. J. Oper. Res.21(2) (1985b) 206–212. Moreover, this estimate gives less values of the approximation errors than most of the other known estimates. [ABSTRACT FROM AUTHOR]