• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.249-273
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• 1996

This paper reviews and develops several statistical models for extreme values, based on threshold methodology. Extreme values of a time series are modeled in terms of tails which are defined as truncated forms of original variables, and Markov property is imposed on the tails. Tails of the generalized extreme value distribution and a multivariate extreme value distributively, of the tails of the series. These models are then applied to real ozone data series collected in the Chicago area. A major concern is given to detecting any possible trend in the extreme values.

• Atmosphere
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• v.26 no.4
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• pp.697-709
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• 2016

This study estimates and evaluates the extreme value of 30 m-resolution daily maximum and minimum temperatures over South Korea, using inverse distance weighting (IDW), parameter-elevation regression on independent slopes model (PRISM) and generalized extreme value (GEV) method. The three experiments are designed and performed to find the optimal estimation strategy to obtain extreme value. First experiment (EXP1) applies GEV firstly to automated surface observing system (ASOS) to estimate extreme value and then applies IDW to produce high-resolution extreme values. Second experiment (EXP2) is same as EXP1, but using PRISM to make the high-resolution extreme value instead of IDW. Third experiment (EXP3) firstly applies PRISM to ASOS to produce the high-resolution temperature field, and then applies GEV method to make high resolution extreme value data. By comparing these 3 experiments with extreme values obtained from observation data, we find that EXP3 shows the best performance to estimate extreme values of maximum and minimum temperatures, followed by EXP1 and EXP2. It is revealed that EXP1 and EXP2 have a limitation to estimate the extreme value at each grid point correctly because the extreme values of these experiments with 30 m-resolution are calculated from only 60 extreme values obtained from ASOS. On the other hand, the extreme value of EXP3 is similar to observation compared to others, since EXP3 produces 30m-resolution daily temperature through PRISM, and then applies GEV to that result at each grid point. This result indicates that the quality of statistically produced high-resolution extreme values which are estimated from observation data is different depending on the combination and procedure order of statistical methods.

• KIEE International Transactions on Power Engineering
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• v.5A no.3
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• pp.300-302
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• 2005

We employ a new technique to account for extreme values when using the generalized autoregressive conditionally heteroskedastic (GARCH) methodology to forecast day-ahead electricity prices in New York City.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.145-153
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• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.99-106
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• 2008

In this paper, we establish some recurrence relations which is satisfied by the quotient moments of the lower record values from the standard generalized extreme value (GEV) distribution.

• Smart Structures and Systems
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• v.17 no.6
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• pp.995-1015
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• 2016

In the design and condition assessment of bridges, it is usually necessary to take into consideration the extreme conditions which are not expected to occur within a short time period and thus require an extrapolation from observations of limited duration. Long-term structural health monitoring (SHM) provides a rich database to evaluate the extreme conditions. This paper focuses on the extrapolation of extreme traffic load effects on bridges using long-term monitoring data of structural strain. The suspension Tsing Ma Bridge (TMB), which carries both highway and railway traffic and is instrumented with a long-term SHM system, is taken as a testbed for the present study. Two popular extreme value extrapolation methods: the block maxima approach and the peaks-over-threshold approach, are employed to extrapolate the extreme stresses induced by highway traffic and railway traffic, respectively. Characteristic values of the extreme stresses with a return period of 120 years (the design life of the bridge) obtained by the two methods are compared. It is found that the extrapolated extreme stresses are robust to the extrapolation technique. It may owe to the richness and good quality of the long-term strain data acquired. These characteristic extremes are also compared with the design values and found to be much smaller than the design values, indicating conservative design values of traffic loading and a safe traffic-loading condition of the bridge. The results of this study can be used as a reference for the design and condition assessment of similar bridges carrying heavy traffic, analogous to the TMB.

• Proceedings of the Korea Information Processing Society Conference
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• 2007.05a
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• pp.870-872
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• 2007

Sensor networks have been widely applied for data collection. Due to the energy limitation of the sensor nodes and the most energy consuming data transmission, we should allocate as much work as possible to the sensors, such as data compression and aggregation, to reduce data transmission and save energy. Querying extreme values is a general query type in wireless sensor networks. In this paper, we propose a novel querying method called Two-Level Filter (TLF) for querying extreme values in wireless sensor networks. We first divide the whole sensor network into domains using the Distributed Data Aggregation Model (DDAM). The sensor nodes report their data to the cluster heads using push method. The advantages of two-level filter lie in two aspects. When querying extreme values, the number of pull operations has the lower boundary. And the query results are less affected by the topology changes of the wireless sensor network. Through this method, the sensors preprocess the data to share the burden of the base station and it combines push and pull to be more energy efficient.

• Wind and Structures
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• v.19 no.3
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• pp.271-294
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• 2014

The impact of artefacts in archived wind observations on the design wind speed obtained by extreme value analysis is demonstrated using case studies. A signpost protocol for detecting candidate artefacts is described and its performance assessed by comparing results against previously validated data. The protocol targets artefacts by exploiting the serial correlation between observations. Additional "sieve" algorithms are proposed to identify types of correctable artefact from their "signature" in the data. In extreme value analysis, artefacts displace valid observations only when they are larger, hence always increase the design wind speed. Care must be taken not identify large valid values as artefacts, since their removal will tend to underestimate the design wind speed.

• Atmosphere
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• v.18 no.4
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• pp.397-416
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• 2008

This study investigates a long-term variation of the annual extreme value for the instantaneous wind speed and the daily precipitation during 56 years (1951-2006) in Korea. Results show that there is a uptrend for both wind and precipitation extreme records, although regional trends are different from overall pattern in some places, particularly for wind speed. The estimated linear trends are 230 mm/56 yr in the daily precipitation and $15ms^{-1}$/56 yr in the maximum instantaneous wind speed. For precipitation, other indexes such as total annual precipitation, the number of extreme precipitation event, and precipitation intensity have dramatically increased as well, while there has been a clear downtrend for the number of strong wind events (> $14ms^{-1}$). It is found that the minimum surface pressure recorded during typhoon attacks in Korea tends to be decreasing, about 10 hPa/56 yr. This partly explains why the extreme values in the precipitation are increasing in Korea.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.250-260
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• 1992

Two methods for computing extreme sea levels, which are the extreme probability method and the joint probability method, are examined at five different ports (Incheon, Cheju, Yeosu, Pusan, Mukho). The extreme probability mothod estimates the extreme sea levels from three different probability papers of Gumbel, Weibull and generalized extreme value(GEV) using the least square method, conventional moment method and probability weighted moment method. respectively. The results showed that the extreme sea levels estimated by the Gumbel paper or the least square method appeared higher than those calculated by other papers or methods. The extreme values estimated by the extreme probability method are approximately 5-10 cm lower than the values by the joint probability method.